Combustion chemistry of COS and occurrence of intersystem crossing

This contribution combines results of experiments with kinetic modelling to probe the unusual behaviour of carbonyl sulfide (COS), a sulfur species that frequently arises in fuel systems. The experiments identified CO and SO2 as the primary oxidation products, with no formation of CO2. The low ignition temperature (<600 K) of COS observed in prior experiments conflicts with the high activation barrier for the reaction COS + O2 → CO2 + SO of 211.3 kJ mol 1 on the traditional triplet reaction surface. We proposed that, this kinetic barrier prompts the reaction to transfer onto the singlet surface through intersystem crossing that allows the process to surmount lower-energy hurdles. By considering the oxidation of COS as a single step reaction, we fitted the Arrhenius parameter for the reaction COS + O2 → CO + SO2 directly from our experimental measurements. The fitted activation energy of 70.1 kJ∙mol 1 agrees with that of 85.4 ± 20.0 kJ∙mol 1 as calculated in literature at the Hartree-Fock level of theory, indicating the appearance of the intersystem crossing process in the oxidation of COS. The reaction mechanism based on this comportment leads to excellent agreement between the kinetic model and the experimentally measured quantities, such as the onset temperature and the conversion profiles of detected species. The proposed kinetic model for the oxidation of COS provides a tool to design both the SOx mitigation processes and industrial systems for safe handling of sulfur impurities in fossil fuels.


Introduction
The presence of sulfur impurities in bio and fossil fuels affects the combustion process, requiring detailed understanding of the oxidation reactions [1] to design air-purification devices to avoid pollution [2,3]. However, present models of sulfur combustion fail to explain the behaviour observed in experiments, especially the flammability and fire hazard of sulfur species. Sulfur may comprise up to several percent by weight in coals [4], natural gas (the so-called sour gas), coal seam gas and syngas [5]. In energy industry, the conversion of H 2 S into solid-state sulfur during Claus treatment leaves small amounts of unconverted CS 2 and COS in natural gas [6][7][8][9]. Significant quantities of CS 2 and COS also materialise during the thermal-oxidative reaction of sulfur-containing species in presence of hydrocarbons, such as in fuel-rich oxidation of methane seeded with H 2 S [10][11][12][13] or during the pyrolysis of ethylene doped with SO 2 [14][15][16][17].
Commercial grades of natural gas contain typically 5.5 mg•m − 3 sulfur species, in which the odourant mercaptan (CH 3 SH) contributes 4.5 mg•m − 3 as indicator of leakage [18]. Further oxidation of CH 3 SH present in natural gas also leads to formation of H 2 S, CS 2 and COS as intermediates in the combustion process [19,20]. Municipal waste releases polyaromatic hydrogen (PAH), NO x , as well as sulfur containing species as pollutants [21][22][23][24] during waste to energy conversion [25].
Additionally, the reduced sulfur species (H 2 S, CS 2 , COS and CH 3 SH) display high flammability and explosion hazard, which demand strict safety procedures during storage, transportation and processing in fuel industry [26]. Especially, the low-cost and environmentally-friendly lithium-sulfur batteries may engender hazards in their manufacturing and recycling, due to the flammability of sulfur species [27][28][29]. In the environment, COS exists as the most abundant sulfur carrier in the atmosphere (>400 ppt) [30,31], with its half-life time estimated at about two years. Plants absorb COS in atmosphere, as a source of sulfur, to produce enzymes including sulfur atoms [32]. Certain kinds of bacteria also deploy the oxidation of inorganic sulfur as a source of energy [33].
Despite the important role of reduced sulfur species in the energy and environmental fields, studies on combustion chemistry of CS 2 and COS remain limited. Since COS appears as an intermediate in the oxidation of CS 2 , the COS/O 2 sub-mechanism imposes a substantial influence on this process [34]. By conducting a critical review and quantum chemical calculations, Glarborg and Marshall proposed a comprehensive oxidation mechanism for COS [35] and CS 2 [36]. The reaction scheme of Glarborg and Marshall overestimates the ignition temperature of both CS 2 and COS as measured in a tubular-flow reactor [37,38], at temperatures below 1400 K, by 260 K and 140 K, respectively, under the stoichiometric condition. This disagreement has important safety implications as CS 2 and COS may appear safer than indicated by their kinetics. Similarly, Abián et al. [39] reported a discrepancy between the predictions from this mechanism and the results of experiments performed under moist atmosphere in a tubular-flow reactor.
We have recently revised the oxidation mechanism of CS 2 , based on the results of both experiments and quantum chemical calculations (at CBS-QB3 level), improving the important elementary reactions [26,40]. Conversion of COS has been captured as a critical intermediate in oxidation of CS 2 [40]. The crossing-over between the triplet (ground state) and singlet (excited state) reaction surfaces prevails in oxidation of reduced sulfur species, including the reactions of 1 [26]. The intersystem crossing (ISC) represents the transition between triplet and singlet pathway, to avoid the high activation barrier on traditional triplet surface, offering lower activation barriers and higher reaction rates at temperatures between 550 and 1200 K. Furthermore, the occurrence of the intersystem crossing in oxidation of S [43], H 2 S [41,42,44] and CS 2 [36] has prompted us to suspect its presence in the oxidation of COS. Our measurements of the oxidation of CS 2 in the jet-stirred reactor required a higher rate for Reaction R1 (where we explicitly denote the triplet species by a digit "3 ′′ written in the superscript) in the subset mechanism of COS/O 2 to match the faster conversion and a lower accumulation of COS as observed in the experiments. The quantum chemistry calculations on both triplet (ground state) and singlet (excited state) pathways also confirm the occurrence of the intersystem crossing for Reaction R1, reducing the activation energy from 134.3 kJ•mol − 1 to 85.4 kJ•mol − 1 [40].
Reaction R1 initially changes its path from a triplet to singlet surface to avoid the activation energy of 134.3 kJ mol − 1 . It then proceeds on the singlet surface until completion to produce 1 CO and 1 SO 2 , both species detected in experiments. While it is possible that, a reaction may switch more than once between two spin surfaces, the results of the experiments tell us that the reaction does not return to its triplet pathway. Had the reaction switched back to the triplet pathway, it would have produced CO 2 and SO . However, we have detected no CO 2 (only CO) in the experiments [40]. This occurred despite the products of the triplet pathway displaying lower energy by 15.4 kJ mol − 1 .
This study conducts direct experimental measurements of oxidation of COS in a jet-stirred reactor (JSR), to further improve our previouslyproposed mechanism for COS oxidation [40]. Using the infrared spectroscopy, we carefully determine the conversion of COS to produce CO and SO 2 , in the industrially-relevant temperature window of 550-1400 K, under ambient pressure and at a constant residence time of 1.88 s. We examine the performance of the previously-proposed kinetic mechanism and conduct a sensitivity analysis on the conversion of COS to identify the governing elementary reactions for its oxidation. Furthermore, by considering the oxidation of COS as a single step reaction, we fit the Arrhenius parameters for Reaction R1 directly from our experimental measurements. Finally, we validate the updated mechanism against the experimental measurements of other researchers and discuss the influence of moisture in the oxidation of COS.

Methodology
The following text provides a concise account of our jet-stirred reactor (JSR) system, with the experimental set-up described in detail in reference [45]. Fig. 1 illustrates the schematic diagram of the apparatus, including the temperature profiles in the electrically-heated single-zone furnace deployed in this study. Table S1 in Supplementary data lists the flow rates implemented in the experiments.
The jet-stirred reactor [46,47], built by Monash Scientific, Melbourne, Australia, incorporates four nozzles, each with 0.3 mm ID, hosted in a spherical space. This design induces a high Reynolds number of around 1990 for the inlet flow through the nozzles into the reactor, providing mixing and eliminating the temperature and species gradients in the reactor [48]. For this reason, the jet-stirred reactor approximates well the ideal continuous stirred tank reactor (CSTR), with CSTR named as the perfectly-stirred reactor (PSR) in the combustion literature [46]. Ultra-high purity quartz (99.99%) is used to construct the reactor to minimise the surface reaction as Wang et al. [49] reported the order of catalytic activity of CaO > Fe 2 O 3 > Al 2 O 3 ≫ SiO 2 (at 313 K) for oxidising CS 2 on atmospheric particles. Additionally, the spherical jet-stirred reactor minimises the surface to volume ratio compared to the tubular flow reactor.
A Fourier transform infrared (FTIR, Perkin Elmer, U.S.) spectrometer facilitated online monitoring and quantitating the gas species exiting JSR, by averaging 8 individual spectra, each requiring approximately 15 s to collect. Thus, each IR spectrum presented in this contribution signifies about 2 min of data acquisition. QASoft software (Infrared Analysis Inc., U.S.) served to quantitate the species concentration, with the following limits of detection (LOD): [SO 2 ] = 5 ppm, [CO] = 20 ppm, [COS] = 9 ppm, using the IR bands for each of these gases (2086.1-2011.6 cm − 1 for COS, 1400.9-1302.2 cm − 1 for SO 2 and 2226.7-2144.7 cm − 1 for CO). Due to the low detection limit of CO, we have also conducted a calibration for the FTIR with standard CO gas (BOC, Australia, see Section S13 in Supplementary data). No CO 2 formed in the experiments, as revealed by lack of detection of this gas at the reactor outlet.
We adopted the COS/O 2 sub-mechanism included in our previous mechanism for CS 2 oxidation [26], which in turn had been based on the work of Glarborg et al. [35,36]. The mechanism involves the improved COS/O 2 subset that features the intersystem crossing. Finally, Chemkin-Pro [50] afforded the implementation of a perfectly stirred reactor to model the species concentrations in the exhaust stream from the reactor, while the sensitivity analysis served to locate the controlling steps for the COS conversion. Because of mixing of its contents, the concentrations of species in the reactor and in the outlet are the same.  [34,38], oxidation of COS does not produce CO 2 . Thus, we define the stoichiometric condition for the oxidation of COS as:

Experimental results for oxidation of COS
The oxidation of COS commences at a significantly low temperature. Under the stoichiometric condition (λ = 1.00) and the residence time of 1.88 s, the oxidation (Fig. 2) sets off at 610 K, with COS completely converted to CO and SO 2 at around 1230 K. For the fuel-lean mixture (λ = 1.30, Fig. S1(a)), the reaction arises at 570 K and finalises at 1190 K; i. e., at a lower temperature than for the stoichiometric condition, because of the abundance of oxygen. However, under the fuel-rich condition (λ = 0.70, Fig. S1(d)), no complete conversion of COS comes to pass at temperatures up to 1310 K. For temperature above 1210 K, we highlight a significant drop in the concentration of COS that occurs after the complete depletion of O 2 (as illustrated in Fig. S2(b) in Supplementary data). This is because, for temperatures above 1210 K, the pyrolysis process prompts the further consumption of COS.
We conducted three repeat experiments for each condition, achieving reproducibility within 5% for the peak absorption of each species for all experimental temperatures and oxygen-fuel equivalence ratios. Supplementary data provide a comparison of the results from these experiments (Table S2). The experimental uncertainty originates from the accuracy of mass flow controllers (2%), the error range for temperature in the reaction zone (±2.5 K), fluctuation of room temperature (295 K-299 K) and the online FTIR measurement of species concentration (±2%) due to background noise. While the error in the concentration of the purchased mixture of COS/N 2 (±30 ppm COS) does not affect the precision of the present measurements, it influences their accuracy. QASoft software [51] enabled the quantitation of COS, CO and SO 2 for all spectra measured with 0.1 m cell. The elemental balances for sulfur and carbon correspond to 100 ± 10% and 100 ± 4%, respectively, with the elevated uncertainty for sulfur due to the unaccounted S formed along the pyrolysis pathway after the depletion of O 2 , in the fuel-rich experiments.

Fig. 3 contrasts the Chemkin modelling results of Glarborg and
Marshall's mechanism [25] with the species concentrations at the outlet from our jet-stirred reactor for the oxidation of COS under stoichiometric λ = 1.00, for fuel-lean (λ = 1.30) and fuel-rich (λ = 0.70) conditions, see Fig. S2 of Supplementary data. The production of CO and SO 2 follows the ratio of 1:1, that is, [CO] ≈ [SO 2 ], as quantitated from the experimental IR spectra of the exhaust gases. This explains why the CO and SO 2 symbols overlap each other in Fig. 3. The equal production rates of CO and SO 2 reinforce the adopted definition of the stoichiometry (Reaction R stoichiometry ). We also express the oxidation of COS as a single   Glarborg and Marshall [35] considered the rate constant of this reaction to be similar to that of CS 2 + O 2 , and estimated it as k R1_est = 1.0 × 10 12 exp (− 134.0 kJ•mol − 1 /(RT)) cm 3 •mol − 1 •s − 1 . However, the experiments involving a tubular-flow reactor for wet oxidation of COS found the mechanism to overestimate the ignition temperature by almost 140 K [39]. The mechanism also results in a high accumulation of COS during the oxidation of CS 2, contradictory to the observations from our JSR experiments [40]. The experimental low ignition temperatures of COS of 570 K (λ = 1.30), 610 K (λ = 1.00) and 630 K (λ = 0.70) in the current work indicate that, the thermal dissociation process, depicted by Reaction R2, cannot act as the chain initiation process. This reaction operates only at high temperatures, at around 1210 K, as indicated by the experiments under the fuel rich conditions.

COS → CO + S (R2)
COS + S → CO + S 2 (R3) The kinetic mechanism (Supplemental data, Part B) does not differentiate between triplet and singlet species, although S, S 2 , O, and SO can exist in both forms in the experiments. There is no experimental or theoretical confirmation whether these products arise in Reactions R3-R5 as triplets or singlets. The combined theoretical and experimental validation of the spin states, as this of the products of Reaction R1, are rare in literature [40]. It stands to reason that future theoretical and experimental studies should focus on determining the spin state of S, S 2 , SO and O arising in Reactions R2-R5.
We conducted a sensitivity analysis on the decreasing concentration of COS at different stages of the oxidation process between 600 K and 1400 K, at intervals of 100 K, with respect to pre-exponential factors of all reactions. As illustrated in Fig. 4, Reaction R1 acts as the controlling step for the oxidation of COS for temperatures below 1100 K, confirming that, the oxidation of COS constitutes a single-step process. At temperature above 1200 K, Reactions R3 and R4 commence to influence the consumption of COS. As mentioned above, the pyrolysis channel R2 kicks in under high temperature (>1200 K), producing S to interact with COS. Atomic S also interacts with O 2 , resulting in O (Reaction R5), which reacts with COS as shown in the sensitivity analysis. No other reactions are reported to affect the consumption of COS within the studied temperature range.

Kinetics of COS + O 2 → CO + SO 2
Since the sensitivity analysis confirmed the oxidation of COS as a single step process proceeding through Reaction R1, we fit the rate parameters directly from our experimental measurements based on the species exiting the JSR: where F COS_in and F COS_out represent the molar flowrate of COS in and out of the reactor (mol•s − 1 ), respectively. The symbol V denotes the volume of the reactor. The reaction rate is evaluated at the outlet conditions by using [COS] out and [O 2 ] out , because of the mixing in the reactor. As demonstrated in Fig. S2(b) in Supplementary data, pyrolysis of COS starts to operate around 1200 K. Hence, we fit k R1 using the measurements acquired below 1150 K, to avoid the error introduced by the influence of the pyrolysis process. With a fixed inlet concentration of COS at 1545 ppm (λ = 1.30), 1548 ppm (λ = 1.00) and 1552 ppm (λ = 0.70), respectively, the online FTIR measures the remaining COS exiting the JSR at different temperature. By employing Eq. 1, we derive the reaction rate k R1 for each temperature (a detailed calculation process and the results appear in Section 7 and Table S3 in Supplementary data). Fig. 5 illustrates the Arrhenius plot of log 10 k R1 versus 1000/T, from 550 K to 1150 K. Within the studied temperature range, the R 2 coefficient of 0.951 indicates good linearity. The reaction rates for the experiments performed under fuelrich condition fall slightly below those calculated from the stoichiometric and fuel-lean measurements. Our mechanism does not account for the existence of minor quantities of COS dimers [52]. The nonlinearity in the high-temperature range (>1200 K) originates from the As expected, the activation energy of 70.1 kJ•mol − 1 agrees with the minimum energy crossing point calculation performed at the HF level of theory to yield 85.4 ± 20.0 kJ•mol − 1 [40], indicating the appearance of an ISC process. The reaction initiates with 1 COS and 3 O 2 both in ground state, however, it transits into the singlet reaction pathway through the crossing-over point between the singlet and triplet energy surfaces, with a barrier around 70.1 kJ•mol − 1 , as illustrated in Fig. S3 in Supplementary material. The occurrence of intersystem crossing relates with spin-orbital coupling of species. The transition is a radiation-less process, which means no energy is released or absorbed. Reactions always prefer to be in the lower energy state even if one of the reactants resides in another spin arrangement; the formation of 1 H 2 O from 1 H 2 and 3 O 2 serves as a notable example. The pre-exponential factor A needs to be smaller than that of a typical collision rate, as it must incorporate the probability of the system crossing from the triplet to singlet surfaces. In our previous work [40], we estimated the pre-exponential factor A to be 3.5 × 10 12 cm 3 •mol − 1 •s − 1 to achieve agreement between our kinetic modelling and the experimental measurements. In this work, the fitted rate constants for Reaction R1 are updated in the oxidation mechanism for carbonyl sulfide. Table 1 summarises the updated rate constants of the reaction revised in this study. Fig. 6 compares the experimental measurements, plotted as symbols, with the results of the kinetic modelling, signified by dashed lines, using the updated mechanism that includes the modification of the Arrhenius parameters for Reaction R1. The comparison illustrates good agreement for the onset temperature and for the trend in the conversion of COS. For the fuel-rich condition of λ = 0.70, the updated kinetic model captures well the pyrolysis above 1210 K, also confirming the robustness of the pyrolysis mechanism.

Validation of updated mechanism with literature data
This section tests the updated mechanism with the experimental measurements of Abián et al. [39] for the moist oxidation of COS in a tubular-flow reactor, discussing the effect of humidity. Direct fission of a H 2 O molecule into H and OH entails a high activation energy of 446 kJ•mol − 1 [53]. The hydrolysis of COS features a moderate activation energy of 152 kJ•mol − 1 , as calculated by Ling et al. [54]. Here, we implement Reaction R6 in our updated mechanism, using the rate parameters calculated by Ling et al. [54], and express the reaction rate as k R6 = 1.5 × 10 13 exp (− 152.4 kJ•mol − 1 /(RT)) cm 3 •mol − 1 •s − 1 . We also include the oxidation mechanism of H 2 S as proposed by Song et al. [55] to offer an exit channel for H 2 S (if produced). To simplify the fluid-dynamic considerations, we model the reactor as perfectly turbulent and perfectly laminar; for the latter, providing the illustrative results along the centreline and near the wall. As expected, the species profiles obtained for the plug flow reactor reside between the two curves corresponding to the laminar conditions, as illustrated in Fig. S5 in Supplementary data. As the differences are small (within 30 K), we base our further discussion on the results obtained for the plug-flow reactor. A plausible explanation for this small difference may stem from high diffusion rates of product species compared to the convective flow rate, as follows from the calculations of the Péclet number for mass transfer, outlined in Supplementary data.
During the oxidation of COS under wet conditions at less than 1000 K, our model predicts no CO 2 formation. Sensitivity analysis concluded that, Reaction R6 does not operate over the entire temperature window of the present study. This also means that, moisture does not affect the combustion chemistry of COS, in agreement with the analogous behaviour observed in combustion of natural gas [56]. At temperatures in excess of 1025 K, one observes the conversion between CO and CO 2 . Both modelling and experiments capture well this comportment.
The present mechanism improves the onset temperature for the oxidation of COS from 1160 K (Abián's et al. model) to 940 K (this work), because of the increased rate induced by the updated constants of Reaction R1. However, our model under-estimates the ignition points by 80 K compared to the experimental results. Two possible explanations are provided here: (1) The updated reaction rate of R1 based on experiments at 600 K-800 K in a jet-stirred reactor involves a higher ratio of singlet pathway with lower activation energy. With ignition temperature increasing to 1000 K in tubular flow reactor (TFR), the triplet pathways become the predominant channel for the reaction of COS + 3 O 2 that displays a higher activation barrier, thus, leading to a higher reaction rate as expected. Fig. S6 in Supplementary data illustrates a comparison of the COS fraction at the outlet of the modelled reactors as a function of the temperature, either for a singlet or triplet pathway, as calculated in [40]. The experimental results fall between the modelling results obtained for the singlet and triplet pathways, respectively. The ratio between these two channels, through intersystem crossing,  deserves further study.
(2) With a higher surface to volume ratio, the quartz surfaces in the tubular flow reactor (TFR) could remove more radical species than those in the jet-stirred reactor (JSR), thus inhibiting the ignition of COS. Fig. S7 in Supplementary data displays a semiquantitative estimation of the effect of removal of radicals by the reactor walls on the mole fraction of species at the reactor outlet. In future, we expect more studies of COS oxidation, reporting oxidation of COS on catalytic surfaces and detailed theoretical calculations of intersystem-crossing, to fill the gap between modelling prediction and experimental measurements.

Conclusions
This contribution reported new experimental measurements for oxidation of COS from a jet-stirred reactor system operated in the temperature range from 550 K to 1400 K at a fixed residence time of 1.88 s, under atmospheric pressure, and oxygen-fuel equivalence ratio λ of 0.70, 0.85, 1.00, 1.15 and 1.30. Through kinetic modelling, the sensitivity analysis for [COS] Out located the controlling step for oxidation (Reaction R1: 1 COS + 3 O 2 → 1 CO + 1 SO 2 ) of COS. By considering the oxidation of COS as a single step reaction, we fitted the Arrhenius expression of k R1 = (3.0 ± 0.3) × 10 12 × exp(− 70.1 ± 2.9 kJ•mol − 1 / (RT)) cm 3 •mol − 1 •s − 1 , from 550 K to 1150 K. As expected, the fitted activation energy of 70.1 kJ•mol − 1 agrees with the outcome of the crossing-point calculation performed at the Hartree-Fock level of theory, between the triplet and singlet pathways of 85.4 ± 20.0 kJ•mol − 1 , as reported in literature. We have also validated the updated mechanism with the results of experiments conducted using a tubular-flow reactor in the presence of moisture and discussed the influence of H 2 O on the oxidation of carbonyl sulfide. The effect of moisture is limited to the conversion of CO to CO 2 at temperatures in excess of 1025 K. The proposed kinetic model for the oxidation of COS will assist in the design of SO x mitigation processes and in the development of safe industrial systems for extracting sulfur impurities from fossil fuels. We also highlight the occurrence of the inter-system crossing process in the oxidation of COS, as investigated in this work and the previous publication. Attention should be paid to the crossing-over between electronic states when examining the oxidation processes of sulfur-containing species. We recommend future calculations to be performed at a higher level of theory, to locate the crossing-over points, as well as to experimentally detect and establish the spin states of S, S 2 , SO and O.