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Klippenstein, Stephen J.

Publications and source records attributed to Klippenstein, Stephen J..

34 records · Page 2

Theoretical Kinetics Predictions for Reactions on the NH 2 O Potential Energy Surface

Recent modeling studies of ammonia oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies among the existing literature mechanisms. In this study, high-level theoretical kinetics predictions have been obtained for reactions on the NH 2 O potential energy surface, including the NH 2 + O, HNO + H, and NH + OH reactions. These reactions have previously been highlighted as important reactions in NH 3 oxidation with high sensitivity and high uncertainty. The potential energy surface is explored with coupled cluster calculations, including large basis sets and high-level corrections to yield high-accuracy (~0.2 kcal/mol 2σ uncertainty) estimates of the stationary point energies. Variational transition state theory is used to predict the microcanonical rate constants, which are then incorporated in master equation treatments of the temperature- and pressure-dependent kinetics. For radical–radical channels, the microcanonical rates are obtained from variable reaction coordinate transition state theory implementing directly evaluated multireference electronic energies. The analysis yields predictions for the total rate constants as well as the branching ratios. We find that the NO + H 2 channel contributes 10% of the total NH 2 + O flux at combustion temperatures, although this channel is not included in modern NH 3 oxidation mechanisms. Modeling is used to illustrate the ramifications of these rate predictions on the kinetics of NH 3 oxidation and NO x formation. Finally, the present results for NH 2 + O are important for predicting the chain branching and formation of NO in the oxidation of NH 3 and thermal DeNO x .

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OH Roaming and Beyond in the Unimolecular Decay of the Methyl-Ethyl-Substituted Criegee Intermediate: Observations and Predictions

Alkene ozonolysis generates short-lived Criegee intermediates that are a significant source of hydroxyl (OH) radicals. Here this study demonstrates that roaming of the separating OH radicals can yield alternate hydroxycarbonyl products, thereby reducing the OH yield. Specifically, hydroxybutanone has been detected as a stable product arising from roaming in the unimolecular decay of the methyl-ethyl-substituted Criegee intermediate (MECI) under thermal flow cell conditions. The dynamical features of this novel multistage dissociation plus a roaming unimolecular decay process have also been examined with ab initio kinetics calculations. Experimentally, hydroxybutanone isomers are distinguished from the isomeric MECI by their higher ionization threshold and distinctive photoionization spectra. Moreover, the exponential rise of the hydroxybutanone kinetic time profile matches that for the unimolecular decay of MECI. A weaker methyl vinyl ketone (MVK) photoionization signal is also attributed to OH roaming. Complementary multireference electronic structure calculations have been utilized to map the unimolecular decay pathways for MECI, starting with 1,4 H atom transfer from a methyl or methylene group to the terminal oxygen, followed by roaming of the separating OH and butanonyl radicals in the long-range region of the potential. Roaming via reorientation and the addition of OH to the vinyl group of butanonyl is shown to yield hydroxybutanone, and subsequent C–O elongation and H-transfer can lead to MVK. A comprehensive theoretical kinetic analysis has been conducted to evaluate rate constants and branching yields (ca. 10–11%) for thermal unimolecular decay of MECI to conventional and roaming products under laboratory and atmospheric conditions, consistent with the estimated experimental yield (ca. 7%).

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Dedication to James A. Miller

This special memorial issue pays tribute to James (Jim) A. Miller, a giant of combustion science who died in 2021, with a celebration of his enormous influence on the field. We were touched by the responses we received after we sent out the invitations for it. Jim inspired several generations of scientists, who viewed him as a mentor, a father figure, and a friend. Together with Nils Hansen and Peter Glarborg, we have written a detailed account on his life and work. Furthermore, it appeared in this journal shortly after his death; and so here we focus on the scientific areas he had interest in and influence on, and how they relate to the 34 papers in this issue. The topics of these papers span a variety of Jim's interests including nitrogen chemistry, polycyclic aromatic hydrocarbon (PAH) chemistry, oxidation chemistry, energy transfer, prompt dissociations, and codes to facilitate combustion chemistry simulations.

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Group additivity values for entropy and heat capacities of C 2 –C 8 alkanes, alkyl hydroperoxides, and their radicals

Group additivity values for the thermodynamic properties of oxygenated radicals are poorly determined due to the absence of high quality reference data. Here, a set of 58 group additive values (GAV) for the standard entropy and heat capacity of relevance to alkane oxidation is derived from fits to an extensive and accurate database of standard entropies (298.15 K) and heat capacities (300–3000 K) recently calculated with the “STAR-1D” formalism. The 192 species in this database represent the alkanes (RH), alkyl radicals ($\dot{R}$), alkyl hydroperoxides (RO 2 H), alkyl-peroxy (R$\dot{O}$ 2 ) and hydroperoxy-alkyl ($\dot{Q}$OOH) radicals for all of the isomers of C 2 –C 5 alkane fuels and a select number of isomers of C 6 –C 9 species. The STAR-1D thermochemical data for this set of species was previously obtained from a coupling of scaled B2PLYPD3/cc-pVTZ vibrational analyses with scaled ωB97X-D/cc-pVTZ one-dimensional hindered rotor corrections. The 2σ uncertainties in the GAV results relative to the STAR-1D data set are 2.4 cal K –1 mol –1 for the entropies and at most 2.0 cal K –1 mol –1 for the heat capacities in the temperature range 500–800 K. The 2σ fitting uncertainties in the heat capacity gradually reduce at higher temperatures reaching a value of 0.8 cal K –1 mol –1 at 2000 K decreasing to only 0.5 cal K –1 mol –1 at 3000 K. The high degree of accuracy for the GAV representations is obtained through the introduction of various new group terms, together with the re-optimization of existing group terms. Among the full set of 58 GAV terms, 25 include non-next-nearest neighbor interactions (NNI) and β-corrections. The updated GAVs can be applied in the prediction of entropies and heat capacities for a wide range of hydrocarbons and hydroperoxide species and their radicals, which is important to the accurate prediction of fuel reactivity at low-temperatures in the range 600–1000 K.

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Radical–Radical Reactions in Molecular Weight Growth: The Phenyl + Propargyl Reaction

The mechanism for hydrocarbon ring growth in sooting environments is still the subject of considerable debate. The reaction of phenyl radical (C 6 H 5 ) with propargyl radical (H 2 CCCH) provides an important prototype for radical–radical ring-growth pathways. We studied this reaction experimentally over the temperature range of 300–1000 K and pressure range of 4–10 Torr using time-resolved multiplexed photoionization mass spectrometry. We detect both the C 9 H 8 and C 9 H 7 + H product channels and report experimental isomer-resolved product branching fractions for the C 9 H 8 product. We compare these experiments to theoretical kinetics predictions from a recently published study augmented by new calculations. Here, these ab initio transition state theory-based master equation calculations employ high-quality potential energy surfaces, conventional transition state theory for the tight transition states, and direct CASPT2-based variable reaction coordinate transition state theory (VRC-TST) for the barrierless channels. At 300 K only the direct adducts from radical–radical addition are observed, with good agreement between experimental and theoretical branching fractions, supporting the VRC-TST calculations of the barrierless entrance channel. As the temperature is increased to 1000 K we observe two additional isomers, including indene, a two-ring polycyclic aromatic hydrocarbon, and a small amount of bimolecular products C 9 H 7 + H. Our calculated branching fractions for the phenyl + propargyl reaction predict significantly less indene than observed experimentally. We present further calculations and experimental evidence that the most likely cause of this discrepancy is the contribution of H atom reactions, both H + indenyl (C 9 H 7 ) recombination to indene and H-assisted isomerization that converts less stable C 9 H 8 isomers into indene. Especially at low pressures typical of laboratory investigations, H-atom-assisted isomerization needs to be considered. Regardless, the experimental observation of indene demonstrates that the title reaction leads, either directly or indirectly, to the formation of the second ring in polycyclic aromatic hydrocarbons.

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High-Accuracy Heats of Formation for Alkane Oxidation: From Small to Large via the Automated CBH-ANL Method

It is generally challenging to obtain high-accuracy predictions for the heat of formation for species with more than a handful of heavy atoms, such as those of importance in standard combustion mechanisms. To this end, we construct the CBH-ANL approach and illustrate that, for a set of 194 alkane oxidation species, it can be used to produce ΔH f (o K) values with 2σ uncertainties of 0.2-0.5 kcal mol -1 . This set includes the alkanes, hydroperoxides, and alkyl, peroxy, and hydroperoxyalkyl radicals for 17 representative hydrocarbon fuels containing up to 10 heavy atoms with various degrees of branching in the alkane backbone. The CBH-ANL approach, automated in the QTC and AutoMech software suites, builds balanced chemical equations for the calculation of ΔH f (o K), in which the reference species may be up to five heavy atoms. The high-level ANLo and ANL1 reference ΔH f (o K) values are further refined for even the largest of these reference species with a novel laddering approach. We perform a comprehensive quantification of the uncertainties for both the individual reference species (the largest of which is 0.15 kcal mol -1 ) and the propagation of those uncertainties when used in the calculation of ΔH f (o K) for the 194 target species. Here we examine the sensitivity of the predicted ΔH f (o K) values to (i) electronic energies from various methods, including ωB97X-D/cc-pVTZ, B2PLYP-D3/cc-pVTZ, CCSD(T)-F12b/cc-pVDZ-F12//B2PLYP-D3/cc-pVTZ, and CCSD(T)-F12b/cc-pVTZ-F12//B2PLYP-D3/cc-pVTZ; (ii) the zero-point vibrational energies (ZPVEs), where we consider harmonic ZPVEs as well as two scaling-based estimates of the anharmonic ZPVEs, all implemented for both ωB97X-D/cc-pVTZ and B2PLYP-D3/cc-pVTZ calculations; (iii) the particular CBH-ANL scheme employed; and (iv) the procedure for choosing the reference conformer for the analyses. The discussion concludes with a summary of the estimated overall uncertainty in the predictions and a validation of the predictions for the alkane subset.

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Systematically derived thermodynamic properties for alkane oxidation

Key combustion properties, such as ignition delay time, show strong sensitivity to the thermochemistry of the main species in the standard radical oxidation pathway at low temperatures (600-1000K). Significant uncertainties persist in current estimates of thermodynamic properties, particularly for the larger species of relevance to common practical fuels. In this article, we use advanced computational schemes to evaluate thermodynamic properties for the fuel, fuel radical, peroxy, hydroperoxy-alkyl radical, and hydroperoxide species for a set of 17 fuels containing up to 9 carbon atoms, and with various degrees of branching in the alkane backbone. The procedure, termed STAR-1D, combines conformer sampling to find the minimum geometry, B2PLYP-D3/cc-pVTZ harmonic frequency evaluations, and omega B97X-D/cc-pVTZ one-dimensional torsional mapping. It includes two physically-based scaling routines: a frequency-dependent scaling to B2PLYP-D3/cc-pVTZ anharmonic frequencies and a scaling of one-dimensional omega B97X-D/ccpVTZ torsional profiles to reproduce the product of the B2PLYP-D3/cc-pVTZ frequencies in the harmonic limit. Substantive comparisons with existing experimental databases, together with careful examinations of key theoretical assumptions, are used to explore the accuracy of the predictions. These computationally intensive explorations of 195 species were facilitated by automated thermochemistry software. Further, high accuracy 0 K heats of formation from a separate study are used with the STAR-1D computations to generate NASA polynomial representations. In addition to their intrinsic value, the present results also provide a reliable database for the optimization of group additivity or machine learning schemes for scaling to larger combustion systems. Towards this end a complementary extensive conformational analysis is carried out for the medium sized species and the thermodynamic properties of the lowest energy hydrogen-bonded and non-hydrogen bonded conformers are contrasted for larger hydroperoxy-alkyl radical species.

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Bimolecular Peroxy Radical (RO 2 ) Reactions and Their Relevance in Radical Initiated Oxidation of Hydrocarbons

The kinetics of peroxy radical (RO 2 ) reactions have been of long-standing interest in atmospheric and combustion chemistry. Nevertheless, the lack of kinetic studies at higher temperatures for their reactions with other radicals such as OH has precluded the inclusion of this class of reactions in detailed kinetics models developed for combustion applications. In this work, guided by the limited room temperature experimental studies on selected alkyl-peroxy radicals and literature theoretical kinetics on the prototypical CH 3 O 2 + OH system, we have performed parametric studies on the effect of uncertainties in the rate coefficients and branching ratios to potential product channels for RO 2 + OH reactions at higher temperatures. Literature kinetics models were used to simulate autoignition delays, laminar flame speeds, and speciation profiles in flow and stirred reactors for a variety of common combustion-relevant fuels. Inclusion of RO 2 + OH reactions was found to retard autoignition in fuel-lean (φ = 0.5) mixtures of ethane and dimethyl ether in air. The observed effects were noticeably more pronounced in ozone-enriched combustion of ethane and dimethyl ether. The simulations also examined the influence of ozone doping levels, pressures, and equivalence ratios for both ethane and dimethyl ether oxidation. Sensitivity and flux analyses revealed that the RO 2 + OH reaction is a significant sink of RO 2 radicals at the early stage of autoignition, affecting fuel oxidation through RO 2 ↔ QOOH, RO 2 ↔ alkene + HO 2 , or RO 2 + HO 2 ↔ ROOH + O 2 . Additionally, the kinetic stability of the trioxide formed from RO 2 + OH reactions was investigated using master equation analyses. Last, we discuss other bimolecular reactions that are missing in literature kinetics models but are relevant to hydrocarbon oxidation initiated by external radical sources (plasma-enhanced, ozone-enriched combustion, etc.). In conclusion, the present simulations provide a strong motivation for better characterizing the bimolecular kinetics of peroxy radicals.

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A wide range experimental study and further development of a kinetic model describing propane oxidation

This work presents an experimental and kinetic modeling study of propane oxidation. Ignition delay times of propane were measured in a high-pressure shock tube and in rapid compression machines in the temperature range 689 - 1700 K at equivalence ratios of 0.5, 1.0 and 2.0 in 'air', for a wide range of pressures from 20 to 90 bar. CO and H 2 O mole fraction profiles for propane oxidation were measured in a shock tube behind reflected shock waves in the temperature range 1370-1840 K at equivalence ratios of 0.5, 1.0 and 2.0 and at a pressure of approximately 1.3 atm. Moreover, propane oxidation was studied using a jet-stirred reactor coupled to a synchrotron vacuum ultraviolet photoionization mass spectrometer at low temperatures in the range 565 - 690 K and at a pressure of 1 atm. Further, this wide range of experimental datasets for propane oxidation was used to reoptimize and update our previous kinetic mechanisms, AramcoMech3.0 and NUIGMech1.1. In the current mechanism, NUIGMech1.3, the thermo-chemical parameters of all species relevant to low-temperature propane oxidation chemistry, including propyl-peroxyl, hydroperoxyl-propyl, hydroperoxyl-propyl-peroxyl, and carbonyl-hydroperoxide radicals, are updated based on newly calculated values at the CCSD(T)-F12/TZ-F12//B2PLYPD3/TZ///B2PLYP-D3/TZ level of theory. The improvements made in the thermochemical values and in the kinetic parameters for the low-temperature propane oxidation reactions in NUIGMech1.3 result in better model agreement with the new IDTs and speciation data, including carbon monoxide, formaldehyde, propene, acetaldehyde and various minor products such as ethylene, acetic acid, acrolein as well as various hydroperoxide and cyclic ether species.

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The role of energy transfer and competing bimolecular reactions in characterizing the unimolecular dissociations of allylic radicals

Resonantly stabilized radicals (RSR's) such as allylic radicals typically have bond energies exceeding 45 kcal/mol and are therefore reasonably long-lived up to quite high temperatures. Consequently, kinetics of the unimolecular dissociations and bimolecular reactions of these long-lived RSR's assume significance in high temperature chemically reacting systems such as in flames. Our recent analyses (J. Cho et al., Proc. Comb. Inst., 2022) of the uncertainty propagated by the energy transfer parameters for 1-methylallyl (1MA) dissociation to the laminar flame speed, indicates an intricate coupling between the kinetics of 1MA dissociation (chain propagation) and its reaction with H-atoms (chain-termination). Here, this work extends such analyses to other C 3 – C 5 allylic radicals: allyl, 2-methylallyl, 1,1-dimethylallyl, 1,2-dimethylallyl, and 1,3-dimethylallyl. Theoretical kinetics for the C 3 – C 4 allylic radicals were taken from prior literature studies (J.A. Miller et al., J. Phys. Chem., 2008; J. Cho et al., Proc. Comb. Inst., 2022; R.S. Tranter et al., Proc. Comb. Inst., 2017). Potential energy surfaces were newly computed for the dissociations of the larger C5 allylic radicals and the reactions of these radicals with H-atoms. These PES's were then used to calculate rate constants for the relevant unimolecular and bimolecular reactions. Energy transfer has a crucial role to play in these pressure-dependent reactions and therefore the present kinetics calculations relied on a-priori predictions of collisional energy transfer parameters to best characterize the branching between chain propagating unimolecular dissociations of these allylic radicals and chain terminating bimolecular reactions of these RSR's with H-atoms. Prompt dissociations are now established to be a universal feature of free radical dissociations. Here we have also characterized the propensity for prompt dissociations in these more-stable allylic RSR's and their role in combustion simulations.

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Group additivity values for the heat of formation of C 2 –C 8 alkanes, alkyl hydroperoxides, and their radicals

A set of 58 group additivity values (GAV) for the calculation of the heat of formation is derived from an extensive and accurate database of 192 ab initio heats of formation. The ab initio values are from companion calculations at the CCSD(T)–F12/cc-pVTZ-F12//B2PLYPD3/cc-pVTZ level of theory employing second order connectivity based hierarchy reference reactions with ANL energies for the reference species. This database of 192 species consists of alkanes (RH), alkyl radicals ($\dot{\text {R}}$), alkyl hydroperoxides (RO 2 H), alkyl-peroxy (R$\dot{\text {O}}$ 2 ) radicals, and hydroperoxy-alkyl ($\dot{\text {Q}}$OOH) radicals of all of the isomers of C 2 –C 5 alkane fuels and a select set of C 6 –C 8 isomers. The GAV and ab initio based enthalpies for this dataset show excellent agreement, with an estimated 2σ uncertainty of 0.9 kcal mol –1 . Among the 58 GAV terms, 40 are refinements of previously reported terms, while 18 are newly developed. These new GAV terms are mainly non-next-nearest neighbor interactions (NNI) and β-corrections. The inclusion of these new groups significantly improves the accuracy of the GAV estimates of the heats of formation. Finally, the updated GAVs can be used with increased confidence to estimate the heats of formation of combustion relevant hydrocarbons and oxygenated hydrocarbons and their corresponding radicals, which are important in predicting low-temperature chemistry and are critical in the development of accurate chemical kinetic models.

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The influence of thermochemistry on the reactivity of propane, the pentane isomers and $n$-heptane in the low temperature regime

In this study, the influence of thermochemistry on the reactivity of fuels at low temperatures (600–1000 K) is studied here. Specifically, the effect of different sets of thermochemistry on chemical model predictions is explored, where various sets are calculated at different levels of theory in addition to recently updated group additivity values. Experimentally measured ignition delay times for propane, the pentane isomers and n-heptane are simulated using NUIGMech1.2 and replacing the thermochemistry of the low-temperature species with the calculated values. For propane, three different thermochemistry sets were calculated, namely CCSD(T)-F12/TZ-F12//B2PLYP-D3/TZ//B2PLYP-D3/TZ (QM1), CCSD(T)-F12/TZ-F12//B2PLYP-D3/TZ//ωB97X-D/TZ (QM2) and B2PLYP-D3/TZ/ωB97X-D/6-31G*//ωB97X-D/6-31G* (QM3). The QM2 results provide parameters to optimize new group additivity (NGA) values which are used to calculate the fourth set of thermochemistry. The model predictions using these four sets are compared to those using NUIGMech1.2 for propane. As the QM1 and QM2 calculations are expensive, the thermochemistry calculated from the QM3 and NGA calculations are used in the pentane isomer and n-heptane models. For all of the models, it is found that the thermochemistry of the species involved in the low-temperature reaction sequence ($RH$, $\dot{R}$, $RO_2H$, $R\dot{O}_2$, $\dot{Q}OOH$ and $\dot{O}_2QOOH$ species) significantly affect fuel reactivity. The NGA values were developed based on all of these species except $\dot{O}_2QOOH$ radicals. The thermochemistry of $\dot{O}_2QOOH$ species cannot be accurately calculated with the NGA representations due to the importance of non-next-nearest neighbor interactions of –OOH substitution. Further development of the NGA method to capture such interactions is in progress. Overall, the model developed using the NGA thermochemistry shows better agreement with experimental data than the model using thermochemistry from affordable and prominent QM methods, such as QM3. Based on the results presented for propane, the pentane isomers and n-heptane, the thermochemistry calculated using the NGA method can be used to model the oxidation of higher order hydrocarbons at low temperatures.

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Inefficient intramolecular vibrational energy redistribution for the H + HO2 reaction and negative internal energy dependence for its rate constant

Quasiclassical trajectories (QCT) and newly constructed global potential energy surfaces are used to compute thermal and nonthermal rate constants for the H + HO 2 reaction. The thermal QCTs rate constants are up to 50% smaller than transition state theory (TST) rate constants based on the same level of electronic structure theory. This reduction is demonstrated to result from inefficient intramolecular vibrational energy redistribution (IVR) in the transient H 2 O 2 well, with a significant fraction of trajectories that reach the H 2 O 2 well promptly dissociating back to reactants instead of via the heavily statistically favored 2OH channel. The nonstatistical reduction factor, κ IVR , that quantifies this effect is shown to increase in importance with temperature, with κ IVR = 0.81 at 300 K and 0.47 at 2500 K. Finally, we show that inefficient IVR causes H + HO 2 rate constants mediated by H 2 O 2 to depend inversely on the initial vibrational excitation of HO 2 .

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The role of collisional energy transfer in the thermal and prompt dissociation of 1-methyl allyl

Collisional energy transfer plays a pivotal role in a-priori calculations of the pressure-dependent rate constants obtained from a master equation. However, accurate determinations of collisional energy transfer parameters are rare and so most kinetic studies rely on best-fits of these parameters to experimental measurements (if available) or estimates guided from literature studies. In this work, we have quantified the effect of the uncertainty in energy transfer parameters on the thermal and prompt dissociation kinetics of a resonance stabilized radical, 1-methyl allyl (1MA), of relevance to the combustion of 1- and 2-butene isomers. Simulations using literature kinetics models were performed to assess the impact of these uncertainties on flame propagation and speciation data in laminar flames of 1- and 2-butene. Analyses of the uncertainty propagated by the energy transfer parameters for 1MA dissociation to the flame simulations, in particular the laminar flame speed, indicate an intricate coupling between the kinetics of 1MA dissociation (chain propagation) and its reaction with H-atoms (chain-termination). Ab-initio based theoretical calculations were also performed to obtain pressure-dependent kinetics for the reaction of 1MA with H-atoms. Lastly, theoretically calculated energy transfer parameters were used to best characterize the kinetics and branching between the chain propagating 1MA dissociation and the chain-terminating reaction 1MA + H.

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Methanol oxidation up to 100 atm in a supercritical pressure jet-stirred reactor

Methanol (CH 3 OH) has attracted considerable attention as a renewable fuel or fuel additive with low greenhouse gas emissions. Methanol oxidation was studied using a recently developed supercritical pressure jet-stirred reactor (SP-JSR) at pressures of 10 and 100 atm, at temperatures from 550 to 950 K, and at equivalence ratios of 0.1, 1.0, and 9.0 in experiments and simulations. Here, the experimental results show that the onset temperature of CH 3 OH oxidation at 100 atm is around 700 K, which is more than 100 K lower than the onset at 10 atm and this trend cannot be predicted by the existing kinetics models. Furthermore, a negative temperature coefficient (NTC) behavior was clearly observed at 100 atm at fuel rich conditions for methanol for the first time. To understand the observed temperature shift in the reactivity and the NTC effect, we updated some key elementary reaction rates of relevance to high pressure CH 3 OH oxidation from the literature and added some new low-temperature reaction pathways such as CH 2 O + HO 2 = HOCH 2 O 2 (RO 2 ), RO 2 + RO 2 = HOCH 2 O (RO) + HOCH 2 O (RO) + O 2 , and CH 3 OH + RO 2 = CH 2 OH + HOCH 2 O 2 H (ROOH). Although the model with these updates improves the prediction somewhat for the experimental data at 100 atm and reproduces well high-temperature ignition delay times and laminar flame speed data in the literature, discrepancies still exist for some aspects of the 100 atm low-temperature oxidation data. In addition, it was found that the pressure-dependent HO 2 chemistry shifts to lower temperature as the pressure increases such that the NTC effect at fuel-lean conditions is suppressed. Therefore, as shown in the experiments, the NTC phenomenon was only observed at the fuel-rich condition where fuel radicals are abundant and the HO 2 chemistry at high pressure is weakened by the lack of oxygen resulting in comparatively little HO 2 formation.

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