Adding Ozone Lowers the Heat for Biofuel Combustion

Ozone injection may lead to cleaner, more efficient internal combustion engines

The Science

Low temperature chemistry (LTC) is a special set of reactions that take place at what chemists consider relatively low temperatures: roughly 400-700 Kelvin (260-800 degrees F). Studying LTC is important to the basic science of chemistry. It is also useful for understanding how internal combustion engines burn fuel. In these engines, the ignition of fuel is surprisingly complex, occurring in two separate steps. This two-step process affects how engines produce harmful emissions. One way to make an LTC reaction faster is to inject ozone into a system. This study examined the use of ozone injection with methyl hexanoate (MHX). Researchers use this substance to study the chemistry of the main components of biodiesel. The study found new ways that combustion can operate at temperatures at the very low end of the LTC range.

The Impact

This research discovered a new combustion process for MHX. It occurs at relatively low temperatures (approximately 440 Kelvin, or 330 degrees F) when small amounts of ozone are added to a mix of MHX and oxygen. This finding can help reduce emissions of soot and nitrogen oxide from internal combustion engines. The results are relevant to both biodiesel and conventional fuel engines. The findings also offer new insights on the chemistry of oxidation. They will also contribute to research on atmospheric chemistry.

Summary

The researchers investigated the reactivity of methyl hexanoate/oxygen mixtures over a temperature range (460-940 Kelvin) in the presence of small amounts of ozone in an externally heated, atmospheric pressure jet-stirred reactor. The researchers identified a previously undetected oxidation regime at temperatures below the typical low-temperature regime (extreme low-temperature combustion or ELTC). The researchers identified key intermediate species using a mass spectrometer and ultraviolet radiation generated by the Chemical Dynamics Beamline of the Advanced Light Source, a Department of Energy (DOE) user facility. The experimental data indicates that the chemistry in the ELTC regime is initiated by thermal decomposition of ozone, followed by reactions from methyl hexanoate by oxygen atoms from the ozone.

There have been many investigations into the oxidation of unsaturated hydrocarbons by ozone. However, investigations into the interactions with molecules without a C=C double bond have been scarce. The observation in this research of a new ELTC regime addresses the societal need for clean combustion, as the addition of ozone enables sustainable oxidation near 500 Kelvin, thus eliminating emission of toxic byproducts such as nitrogen oxide and soot. Furthermore, this work provides atmospheric chemistry researchers with information on the formation pathways of highly oxygenated species that are considered to form secondary organic aerosols, another pollutant. Because ozone is a long-lived air-plasma intermediate, this research also improves understanding of plasma-initiated oxidation processes.

Funding

This work was supported by the DOE Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division, as part of the Gas Phase Chemical Physics Program.

Original Paper Here

Extreme Low-Temperature Combustion Chemistry: Ozone-Initiated Oxidation of Methyl Hexanoate

Authors:

• Aric C. RoussoAric C. RoussoDepartment of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United StatesMore by Aric C. RoussoView Biography
• Ahren W. Jasper
• Yiguang Ju
• Nils Hansen*

Abstract

The accelerating chemical effect of ozone addition on the oxidation chemistry of methyl hexanoate [CH₃(CH₂)₄C(═O)OCH₃] was investigated over a temperature range from 460 to 940 K. Using an externally heated jet-stirred reactor at p = 700 Torr (residence time τ = 1.3 s, stoichiometry φ = 0.5, 80% argon dilution), we explored the relevant chemical pathways by employing molecular-beam mass spectrometry with electron and single-photon ionization to trace the temperature dependencies of key intermediates, including many hydroperoxides. In the absence of ozone, reactivity is observed in the so-called low-temperature chemistry (LTC) regime between 550 and 700 K, which is governed by hydroperoxides formed from sequential O₂ addition and isomerization reactions. At temperatures above 700 K, we observed the negative temperature coefficient (NTC) regime, in which the reactivity decreases with increasing temperatures, until near 800 K, where the reactivity increases again. Upon addition of ozone (1000 ppm), the overall reactivity of the system is dramatically changed due to the time scale of ozone decomposition in comparison to fuel oxidation time scales of the mixtures at different temperatures. While the LTC regime seems to be only slightly affected by the addition of ozone with respect to the identity and quantity of the observed intermediates, we observed an increased reactivity in the intermediate NTC temperature range. Furthermore, we observed experimental evidence for an additional oxidation regime in the range near 500 K, herein referred to as the extreme low-temperature chemistry (ELTC) regime. Experimental evidence and theoretical rate constant calculations indicate that this ELTC regime is likely to be initiated by H abstraction from methyl hexanoate via O atoms, which originate from thermal O₃ decomposition. The theoretical calculations show that the rate constants for methyl ester initiation via abstraction by O atoms increase dramatically with the size of the methyl ester, suggesting that ELTC is likely not important for the smaller methyl esters. Experimental evidence is provided indicating that, similar to the LTC regime, the chemistry in the ELTC regime is dominated by hydroperoxide chemistry. However, mass spectra recorded at various reactor temperatures and at different photon energies provide experimental evidence of some differences in chemical species between the ELTC and the LTC temperature ranges.

Introduction:

The low-temperature chemistry of gas-phase oxidation processes (∼500–700 K) has been found to be quite intriguing and has been a long-standing research topic of the combustion community. (1−4) In this temperature range, there can be enough energy in the system to initiate a complex mixture of radical chain propagating, branching, and terminating reactions. This reaction network, known as low-temperature chemistry (LTC), is governed by peroxide species and centered around reactions of radical species R· (originating from H abstraction from a reactant RH by OH) with ambient O₂ molecules in a sequence of O₂ addition steps and isomerization reactions: (1−5)

(R1)

(R2)

(R3)

(R4)

(R5)

₂ can also occur leading to highly oxygenated intermediates that follow similar reaction schemes as described in

(R6): (4,5)

(R7)Reactions R2, (R4), and (R7) are referred to as first, second, and third O₂ addition reactions, respectively.

A different chemical phenomenon occurs when the temperature increases beyond ∼700 K. In this temperature range, the equilibrium of the O₂ addition and isomerization pathways shifts back to the reactants, and competing pathways become energetically favorable that form less-reactive intermediates: (4,6)

(R8)(R9)(R10)

Recent examples from Rotavera’s lab include work on ethyloxirane, 2,2-dimethyloxirane, and cyclohexene. (7−9) As such, a so-called “negative temperature coefficient” (NTC) regime is formed in which the reactivity of the system counterintuitively decreases with increasing temperatures. (10,11)These known chemical phenomena impact real-world applications such as internal combustion engines. (12−14) Since Semenov and others first described the basics of the underlying chemical mechanism, (15) it has been known that most complex hydrocarbon and bioderived oxygenated fuels have not a single ignition point but, rather, a two-stage ignition process with a rather lengthy initiation delay between these two ignition regimes. This lag makes up a significant component of the overall ignition delay time, that is, the time between the energy input into a combustible mixture and the initiation of the flame propagation. Mismanaging ignition delay is a key cause of engine failure, through either premature autoignition or ignition of hot spots ahead of the ignition front leading to detonation waves in the combustion chamber—otherwise known as engine knock. (16−18) In addition, these two-stage ignition processes also induce different low-temperature burning regimes such as cool and warm flames. (19) As such, understanding and eventually controlling this two-stage ignition process is of vital importance, because new engine designs with much cleaner emission profiles rely on “chemically controlled” hybrid cycles. These designs lack the spark ignition that is used in Otto cycle engines and use leaner mixtures to keep temperatures low and prevent NO_x formation, and they premix or partially premix charges before autoignition to prevent incomplete combustion and the formation of soot and other harmful particulates that occurs due to diesel spray injection. (20−24) To make these new reaction-controlled engines function, and to meet various governments pushing toward strict emission controls, (14,25) the ability to model, predict, and control fuel ignition behavior is a key concern, and additional chemical kinetics research can help to meet these goals.Methods of accelerating these low-temperature ignition processes without resorting to higher temperatures are being explored. (26−31) Especially, various forms of nonequilibrium plasmas, created through radio frequency (RF), microwave, and nanosecond-pulsed discharges, are being investigated to produce active species for kinetic acceleration (as opposed to heating). Such plasmas interact with the combustion process in multiple ways and can be used either directly in engines or located upstream to dissociate or upconvert fuels into species with greater reactivity at low temperature. (32−34) In particular, the energetic electrons in plasmas, through collisions with the present atoms and molecules, can cause excitation (electronic, vibrational, and rotational), dissociation, and ionization without much exothermic heat release. Through the introduction of plasma-produced highly reactive radical species, a significant decrease in ignition delay time and ignition temperatures can be achieved. (35−39) Reactions can occur at temperatures and fuel mixtures below the flammability thresholds, (40−43) and flames can be stabilized past blow-off limits. (44−47) Diffuse discharges are especially effective for larger-scale ignition kernels and bulk effects without much temperature rise, (48) but there are still many challenges remaining before implementation in real engines. For example, these plasmas also dissociate nitrogen, leading to increased NO_x formation, and diffuse discharges are difficult to generate at pressures greater than 1 atm. As such, some studies have utilized plasmas to generate energetic species such as ozone (O₃), (49−51) which is stable at low temperature and can be transported to the reaction zone for increased reactivity. Indeed, ozone is one of the most prevalent and longest-lived plasma-generated species. It has been demonstrated that the addition of ozone can be used, similar to plasmas, to stabilize flames at below normal flammability limits. (52) The addition of ozone can also accelerate first-stage chemistry to allow for the stabilization of cool flames in laboratory conditions to increase LTC reactivity (53,54) and reduce deflagration to detonation transition times for detonation engines. (54−57)Ozone can conceivably participate in two chemical reaction networks. First, ozone reacts energetically and spontaneously with any species with a C═C double bond, in a process known as ozonolysis. (58,59) Ozone will cleave the double bond and form a cyclic ring structure known as primary ozonide, which subsequently breaks down into a highly reactive Criegee intermediate (CI). The elusive CI itself was detected only recently. (60−64) It is understood that ozonolysis pathways are vital for understanding atmospheric chemistry cycles, as the interactions of ozone with unsaturated hydrocarbons leads to secondary aerosol formation. (65−70) Fundamental, combustion-relevant studies of ozone-initiated and assisted oxidation have focused on simple reactants, such as ethylene (71−74) and cyclohexene, (75−77) where, based on the symmetric structures of the reactants, reaction networks can be assumed a priori based on the expected pathways, and most species are small enough for an absolute concentration measurement. In a recent study, He et al. explored the ozone-initiated oxidation of methyl crotonate, (78) a reactant that can lead to two distinctly different CIs, thus increasing the complexity of the reaction network.Second, ozone is only a metastable plasma species. Temperatures above 450 K are sufficient to thermally decompose ozone, with complete degradation by 600 K, resulting in atomic O and O₂.(R11)This atomic O radical is highly reactive and can affect combustion chemistry at these low temperatures by bypassing much of the induction radical + O₂ chemistry required for an initial radical pool and chain-branching reactions. (52) As such, much of this O atom chemistry should have drastic effects and cause reactivity both above and below the LTC regime. At temperatures below the LTC regime (400–500 K), at which the reactants have typically very low reactivity, it is conceivable that the addition of O atoms can accelerate or initiate the reactivity, while at temperatures above the LTC there should be a suppression of NTC behavior due to the availability of chain-branching pathways. These effects have recently been explored for a small reactant such as dimethyl ether (DME). (54)This paper focuses on the acceleration of the low-temperature chemistry of methyl hexanoate [MHX, CH₃(CH₂)₄C(═O)OCH₃] via ozone addition. There has been only limited work on the interaction of biofuels with chemical accelerants, and little is known about the governing reaction network; this study, which builds upon our earlier work on ethylene, methyl crotonate, and DME interactions with ozone, (54,72,73,78) attempts to close this knowledge gap. MHX was chosen for several reasons. MHX is a typical compound surrogate used to study the oxidation chemistry of long-chain, vegetable-based, fatty acid methyl esters (FAME), which are the main components of today’s biodiesel. (10,79) It has been argued that biodiesel, and nonpetroleum-based biofuels in general, are promising for carbon-neutral energy production. (13) It is also the simplest methyl ester that presents a strong cool flame behavior under the accessible experimental conditions. (80−82) That is, the carbon chain is long enough to allow for radical isomerization reactions via low-strain cyclic transition states.Through the use of an atmospheric pressure jet-stirred reactor equipped with a molecular-beam mass spectrometer, comparisons of the MHX LTC chemistry with and without the accelerated oxidation due to ozone addition were performed over a wide range of temperatures, and key differences in the temperature dependence are discussed here. The results demonstrate that ozone addition initiates oxidation chemistry at temperatures below the LTC region; hence, we refer to it here as “Extreme Low-Temperature Chemistry” or ELTC. We provide evidence that ELTC is not just an extension or “stretching” of the LTC regime but is seen to have some differentiating chemical behavior. Because MHX does not contain a C═C double bond and its oxidation can thus not proceed through the traditional C═C ozonolysis reactions, the newly detected reaction network is distinct from ozonolysis reaction pathways. We provide theoretical evidence for this chemistry being initiated by H abstraction via O atoms. Furthermore, differences in reactivity were also observed in the NTC region in the ozone and the non-ozone cases, further separating this temperature range in the ozone case as its own reactivity region that merits further study.

Experimental Details

The experimental apparatus used to investigate the ozone-initiated low-temperature oxidation of methyl hexanoate is identical to the setup used for the previous measurements on the ozone-triggered low-temperature oxidation chemistry of ethylene and the identification of the Criegee intermediate reaction network. (72,73) A detailed description is provided below, along with a setup diagram seen in Figure 1, to familiarize the reader with the components and settings used for this study. The key elements are a jet-stirred reactor (JSR) and a reflectron time-of-flight mass spectrometer with electron and single-photon ionization capabilities to determine the chemical composition of the gas mixture after molecular-beam sampling.

The JSR is a 33.5 cm³ fused silica sphere that is used to study steady-state gas-phase chemical reactions. Four quartz injector nozzles, with inner diameters of ∼1 mm, are centered within the JSR and create strong stirring jets, which results in a homogeneous mixture both in temperature and species composition. Concentric oxidizer and fuel streams that mix just prior to entering the injectors are regulated upstream by MKS mass flow controllers. By changing the overall mass flow rate, which adjusts the residence time at a constant pressure, the time for reactions can be modified. The reactants’ gas stream is highly diluted by argon to reduce the overall heat of reaction and maintain an isothermal environment. Exhaust gases are removed continuously from the stainless steel pressure vessel housing the experiment, for constant temperature and pressure operation.The reactor is enclosed within an oven, and a range of temperature experiments allow for the determination of the temperature dependence of species concentrations. Temperature is monitored by two thermocouples (K-Type, Thermocoax), one placed just outside the JSR body and another along the quartz nozzle leading to the molecular beam mass spectrometer (MBMS) to monitor the sampling vicinity. At the exit of the JSR, the reaction intermediates and products are sampled through a quartz nozzle with a 40° cone angle and an ∼50 μm tip diameter into the custom-built reflectron time-of-flight mass spectrometer.

The reactor was operated from 460 to 940 K at a constant pressure of 700 Torr. A nominal residence time of τ = 1.3 s and a stoichiometry of ϕ = 0.5 with 80% argon dilution (1% methyl hexanoate, 19% O₂, 80% Ar mole fraction) was used for all cases. An ozone concentration of 1000 ppm was used for the ozone experiments. The 1.3 s residence time was sufficient for adequate signal-to-noise ratios for trace and highly reactive species as well as to ensure ozone reactivity. Gas mixture flow rates were adjusted to maintain this residence time with increasing temperature for all cases and precorrected to account for a temperature shift from the probe from previous studies. (83−86) The temperature uncertainties from the thermocouple measurements are ca. ±20 K. The previous thermocouple probe data gathered along the centerline of the reactor showed a ±5 K variation for dilution levels as low as 80% Ar and at residence times up to 4 s, demonstrating reactor temperature homogeneity. (87,88)For ozone production, a fraction of the oxidizer stream is fed through a corona discharge ozone generator (Oriel) and a 70 cm quartz absorption cell prior to the JSR assembly. A helium–neon UV calibration lamp is used along with an Ocean Optics spectrometer for O₃ concentration measurements at 312.57 nm. With the known ozone absorption cross sections, (89) the ozone concentration as a function of oxygen flow rates through the generator is calibrated and continuously monitored during the experiments.To enable the quantitative determination of the reactor’s composition, including the reactive radical species, and to avoid alterations of the composition before the measurement is conducted, the sampled gases are rapidly cooled in a molecular beam expansion to “quench” any remaining reactions and prevent changes in the chemical composition. In the experiments described here, a small quartz sampling nozzle (∼50 μm) is used as the sampling device, feeding into a low-pressure chamber (10^–4 Torr). This rapid expansion from near-atmospheric experimental conditions to such low pressure both cools the sample and causes the molecules to undergo a supersonic free-jet expansion. A skimmer then samples from the center of this expansion to avoid boundary interactions and regions of less efficient cooling. This subsample enters an even lower pressure chamber (10^–6 Torr) as a molecular beam and, thus, experiences a narrow velocity distribution, few collisions between molecules, and limited chances to react between initial sampling and subsequent analysis.Mass spectrometry techniques have been in use for many decades as a sophisticated tool to investigate the composition of complex gas mixtures. Its widespread use is due to the ability to detect all species (up to a system-specific detection limit) for a mixture without any prior knowledge of the chemical composition. Through various means of ionization and methods of separation, a mass-to-charge ratio plot can be generated, which for most types of mass spectrometry can be simplified to just mass, as the ions are singly charged. Additional techniques building on this fundamental principle, such as tandem mass spectrometry, (90,91) photoelectron photoion coincidence (PEPICO), (92) and the technique used in this paper, single-photon ionization via vacuum-ultraviolet (VUV) radiation, (93,94) have been developed to provide structural information on the molecules in question as well. Combining this structural information with modeling and simulation enables understanding of critical chemical species, formation pathways, and reaction networks. (87,88,95)The MBMS system used in this study is capable of both electron ionization (EI) and photionization (PI) measurements. The non-ozone data were recorded using the EI technique, while PI was used for the ozone-doped experiments. The EI system utilizes an electron gun, which can generate electrons in a wide range of energies. The width of the electron energy distribution is ∼2 eV (full width at half-maximum (fwhm)), which leads to high-energy electrons causing fragmentation of larger and/or less stable species. These fragments then contaminate smaller species spectra, as the signal is now a convolution of what is measured from the experiment and fragments from larger species, which needs to be considered in the data analysis procedures when obtaining quantitative species information. (96,97) The broad nature of the distribution also “smears” the measured appearance energy of any given species, making identification of structures challenging.Many of these challenges can be eliminated when using synchrotron-generated vacuum ultraviolet (SVUV) radiation for ionization, which provides a more robust method to obtain structural information from mass spectrometry data. Using a synchrotron such as the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory (LBNL), high photon flux (10¹⁴ photons/s) and narrow bandwidth energy photons [E/ΔE (fwhm) ≈ 250–400] can be generated with a wide range of energies from 7.4 to 30 eV. (94) This narrow bandwidth and ease of tunability allows for near-threshold photoionization, which minimizes fragmentation in the mass spectra, thus facilitating easy interpretation. Furthermore, by scanning the photon energy, photoionization efficiency (PIE) curves can be recorded, which allow for isomer-specific ionization thresholds at a given m/z ratio. While this experimental technique is very powerful for the identification of small molecules when only a limited number of possible isomers is conceivable, limitations exist for the identification of isomeric structures containing more than seven or eight heavy (C/O) atoms. (73,95,98) Given this concern, we will not discuss species identification here in detail, and, instead, we just point out that the observed peaks in the mass spectra are consistent with the generally accepted oxidation scheme at the low-temperature chemistry conditions.After ionization of the molecular constituents in the beam expansion, pulsed electric fields are used to redirect the ions through a flight tube onto a microchannel plate (MCP). The time it takes for an ion to reach this detector depends on the ion’s velocity, which correlates with the ion’s specific mass-to-charge (m/z) ratio. The MCP output signal is subsequently digitized using a multichannel scaler. In this reflectron setup, the MBMS has a mass resolution of m/Δm ≈ 4000, which is sufficient to separate C/H/O-containing species based on their exact mass. The MBMS has a sensitivity of ∼1 ppm and a large dynamic range.Routines have been developed to transform the mass spectra into quantitative and potentially even isomer-specific mole fraction profiles for both the EI and PI techniques. (83,86,96) They are based on the known inlet conditions, known ionization cross sections, and C/O atom balances. As part of this work, the MHX photoionization cross section has been measured, and the corresponding data can be found in the Supporting Information. For the EI data (non-ozone case), we limited the quantification efforts to the main species and a couple of small molecules (CH₂O and CH₃OOH) because of the potential issues caused by the dissociative ionization processes. Like in our previous works based on photoionization, (72,83) mole fractions for the main species and many small species with known cross sections were extracted as a function of temperature, as seen in Figure 8b for CH₂O and CH₃OOH. For larger species with unknown photoionization cross sections, every effort was made to remove all experimental factors, as discussed in detail in refs (72and73). Although photoionization cross sections can be calculated theoretically, (83,99−102) it has been demonstrated that the uncertainty is substantial for large molecules, resulting in the data being less useful for future model comparisons and validation. Instead, we present these data in the Supporting Information as mole fraction x cross section—as seen in Figure 8 for the ketohydroperoxide (C₇H₁₅O₅). Once an accurate cross section is determined, this information can be used to obtain accurate concentration measurements from the presented data. Since the cross sections for these larger species tend to be similar, rough comparisons of the strength of this combined value still can be used to provide insight into relative concentrations.

For a thorough analysis of the system, validation, uncertainties, and calibration we refer the readers to refs (83,84,and95).

General Features of Mass Spectra

In our experiments we explore a multidimensional parameter space. Mass spectra are obtained as a function of the temperature (in a so-called temperature scan) or as a function of the energy of the ionizing electrons and photons (in an energy scan). Such multidimensional data sets have been found to be tremendously important for unraveling complex reaction networks. (87,88)

Typical mass spectra, shown in Figure 2, were obtained via VUV single-photon ionization at 11.5 eV (upper spectrum) and with electron ionization at 14 eV (lower spectrum) in the mass-to-charge ratio range from 20 to 200. The observed peaks originate from the ionization of the sampled species (parent ions) and dissociative ionization processes (fragment ions). The observed differences between 600 and 800 K are related to the different reactivity of the methyl hexanoate system at these temperatures, that is, LTC-type oxidation at 600 K and the reduced reactivity in the NTC region. The peaks observed at 800 K are related to the reactant methyl hexanoate; that is, the parent ion at m/z = 130.099 (C₇H₁₄O₂) and the well-known fragment peaks at m/z = 101.060 (C₅H₉O₂), 99.081 (C₆H₁₁O), 87.045 (C₄H₇O₂), and 74.037 (C₃H₆O₂) are clearly visible. At 14.0 eV of electron energy, the O₂ peak at m/z = 31.990 is clearly visible in the mass spectrum at 800 K as well. Although the photoionization mass spectra were obtained for the ozone case, the mass spectra obtained by VUV single-photon and electron ionization are quite similar. Only the intensities vary because of different ionization cross sections.

Figure 2

Figure 2. Typical mass spectra obtained by VUV single-photon ionization (upper row, ozone case) and electron ionization (bottom row, non-ozone case) at 600 K (left) and 800 K (right).To further highlight the complexity of the mass spectra and the level of details that can be obtained, for Figure 3 we enlarge the region between mass 70 and 73. The mass spectrum was taken at 600 K and a photon energy of 12.3 eV, and the observed peaks include pure hydrocarbons as well as various oxygenated intermediates. As can be seen, there are several peaks that can be resolved around each nominal m/z value due to the high resolution of the MBMS system, and they are labeled according to their elemental composition.

Figure 3

Figure 3. High-resolution mass spectrum from m/z = 70–73. Various parent and fragment ions ranging from pure hydrocarbons to oxygenated intermediates are detectable.

The observed mass spectra are functions of both temperature and the energy of the ionizing photons or electrons. By interpreting separate temperature and energy scans, information can sometimes be obtained about the identity of the underlying molecular structure and/or the origin of the dissociative ionization processes. This key benefit of PI-MBMS measurements is visualized in Figure 4, which shows the temperature-dependent signal of C₂H₂ from 450 to 940 K recorded with the EI-MBMS in red [Figure 4a] and two different PI-MBMS temperature scans in blue [Figure 4b], one taken at 12.3 eV (hollow squares) and another at 14.35 eV (solid squares). While the temperature-dependent mass spectra reveal a C₂H₂ signal near 600 K in both the 14 eV EI and 14.35 eV PI scans, the signal is absent when the photon energy is lowered to 12.3 eV. Because acetylene’s ionization threshold of 11.4 eV is below the photon energy of 12.3, a signal should also be present in the 12.3 eV temperature scan, if C₂H₂ was an oxidation product. However, because of its appearance only at higher energies, obviously the observed C₂H₂ signal near 600 K is a fragment generated by the dissociative ionization of a larger species. This explanation suggests that the non-ozone case also does not have C₂H₂ appearing at low temperatures. It is beyond the scope of this paper to comprehensively determine which species are fragmenting to cause this additional signal, but this serves as a good example of eliminating systematic error in the measurements using this powerful technique. The differences between the red and blue curves between 700 and 800 K are related to O atom reactions following ozone thermal decomposition and will be discussed later

Figure 4

Figure 4. (a) Temperature profile of the C₂H₂ signal in the non-ozone case recorded with a nominal electron energy of 14 eV. (b) Temperature profile of the C₂H₂ signal in the ozone case recorded at 12.3 and 14.35 eV. The energy dependence of the signal near 600 K reveals this to originate from dissociative fragmentation processes.

This previous example already shows that the mass spectra also change with the photon energy. This is shown more clearly in Figure 5 for the mass spectra near the nominal mass-to-charge ratio of 132. At 9.65 eV, only the two peaks are observed corresponding to C₅H₈O₄ and C₆H₁₂O₃, but as the photon energy increases, the signal of the ¹⁸O isotopologue of methyl hexanoate C₇H₁₄O¹⁸O becomes visible. For this study, we recorded mass spectra from 9.3 to 10.5 eV in 0.05 eV steps, and the energy-dependent signals are photon-flux corrected and then converted into mass-specific PIE curves.

Figure 5

Figure 5. (a–c) Mass spectra near m/z = 132 at photon energies of 9.65, 9.90, and 10.50 eV. Signal corresponds to C₅H₈O₄ (m/z = 132.042), C₆H₁₂O₃ (m/z = 132.079), and C₇H₁₄O¹⁸O (m/z = 132.105). (d) The mass spectral signal can be compiled to obtain mass-specific PIE curves.

While unique identification of the C₆H₁₂O₃ and C₅H₈O₄ intermediates is not possible based on the PIE curve alone, this approach does allow for mass spectral signal for small molecules to be correlated with isomer-specific molecular structures via observed ionization thresholds and photoionization efficiency curves. This strategy is shown in Figure 6 for the identification of the CH₂O₂ and C₂H₆O intermediates. Combining the high resolution of the mass spectrometer and the PIE curves, three intermediates at the nominal mass of 46 can be identified. The JSR-sampled PIE curve for CH₂O₂ matches the known curve of formic acid identically [Figure 6b], and for C₂H₆O, the sampled PIE curve can best be reproduced by a linear combination of the ethanol and dimethyl ether PIE curve [Figure 6c].

Figure 6

Figure 6. (a) Experimental mass spectrum near m/z = 46 at a photon energy of 11.0 eV and 600 K (symbols) with peaks at CH₂O₂ and C₂H₆O fitted as Gaussian profiles (line). (b) JSR-sampled PIE curve (symbols) is compared with literature-known PIE curve of formic acid (line). (c) JSR-sampled PIE curve for C₂H₆O (symbols) is compared with PIE curves of dimethyl ether, ethanol, and their weighted sum (lines).

These examples demonstrate some of the separation and identification capabilities achieved by this experimental apparatus. The remainder of the paper focuses specifically on how this highly versatile experimental approach, combined with theoretical considerations, can be applied to unravel complex chemical reaction networks in the ozone-assisted oxidation of methyl hexanoate.

Low-Temperature Chemistry of Methyl Hexanoate

Before we discuss the ozone-assisted oxidation of methyl hexanoate in more detail, the current section focuses on its conventional low-temperature chemistry. It has been well-established that methyl hexanoate exhibits a strong LTC region, (80−82) which, as discussed earlier, involves the O₂ addition and isomerization of the reactant to form oxygenated species (R1–R7). (4,5) A simplified oxidation scheme based on only one of six different reactant radicals is outlined in Figure 7. The formation of this radical is likely energetically favored, as this C–H bond is weaker than the others by ∼6 kcal/mol. Indeed, modeling results from Dayma et al. highlight the importance of this radical for the consumption of methyl hexanoate at low temperatures via H abstraction with OH, although pathways via the other radical species cannot be neglected. (80)

Figure 7

Figure 7. Simplified scheme of the first oxidation steps in the LTC oxidation and molecular-weight growth processes of MHX. The reaction network consists mainly of O₂ addition reactions, unimolecular isomerization reactions, and bimolecular reactions with radicals like OH and HO₂. Only one of six initial radicals (R) is shown. OHP = olefinic hydroperoxide, KHP = keto-hydroperoxide, ODHP = olefinic dihydroperoxide, KDHP = keto-dihydroperoxide.

A typical mass spectrum indicative of the reaction network at low temperatures is shown in Figure 2. In Figure 7 we marked in blue the mass-to-charge ratios for which a signal has been observed in this study. The highlighted intermediates or, more precisely, the specific classes of intermediates are characteristic for the molecular-weight growth products from the second and third O₂ addition reactions and the general low-temperature chemistry. Because it is beyond the scope of the present paper to provide a comprehensive data set on mole fractions for the validation of chemically detailed mechanisms for methyl hexanoate low-temperature oxidation and given the unknown EI cross sections, fragmentation patterns, and even isomeric contributions of many of these fragile intermediates, we cannot report reliable absolute mole fractions for those large intermediates. Nevertheless, assuming that the cross sections and dissociative ionization patterns could be similar, rough comparisons of the signal intensities still can provide insight into relative concentrations.

The temperature profiles of the keto-hydroperoxides (KHPs) and the other intermediates characteristic of LTC such as olefinic hydroperoxides, diketones, ketones (cyclic ethers), and hydroperoxides are shown in Figure 8a,b. The reactivity in the range from ∼550 to 700 K is clearly visible, in accordance with earlier experimental work by Dayma et al. and HadjAli. (80,81) Besides those species, other strong indicators for LTC are the profiles of formaldehyde (CH₂O) and methyl hydroperoxide (CH₃OOH), for which ionization cross sections are known, and their mass spectral signal was converted into absolute mole fraction profiles. The corresponding quantitative temperature profiles are shown in Figure 8c.

Figure 8

Figure 8. Temperature profiles of (a) KHPs, (b) olefinic hydroperoxides, diketones, ketones/cyclic ethers, and hydroperoxides, and (c) methyl hydroperoxide and formaldehyde follow the trends typical for LTC behavior. These non-ozone data were taken using EI.

More temperature-dependent profiles, including those of the main species like MHX, H₂O, CO, CO₂, and other intermediates, are shown in the next section, in which we compare conventional LTC oxidation schemes with ozone-assisted oxidation reaction networks.

Ozone-Initiated Oxidation

There is evidence in the mass spectra and in the temperature profiles that ozone addition has a profound effect on the overall reactivity of the methyl hexanoate oxidation system over a wide temperature range. At temperatures below the low-temperature regime (<550 K) and in the NTC regime (above ∼700 K), we observe an increase in reactivity compared to the conventional, non-ozone case. In this section, we first describe some general trends observed upon the addition of ozone before then examining in more detail the increased reactivity at temperatures below the LTC regime.

General Trends

Figure 9 shows the mole fraction of methyl hexanoate, of the product species H₂O, CO, and CO₂, and of formaldehyde (CH₂O) as a function of temperature for both the ozone and non-ozone cases. Signal intensities (not quantified) of the C₂H₄O intermediates (acetaldehyde and its ethenol isomeric form) are also included.

Figure 9

Figure 9. Mole fractions as a function of temperature for both the ozone (□) and non-ozone (○) cases for (a) methyl hexanoate, (b) water, (c) carbon monoxide, (d) carbon dioxide, and (e) formaldehyde. Signal intensities as a function of the temperature for the ozone and non-ozone cases for C₂H₄O are shown in (f). The closed squares show the temperature-dependent signal of the ethenol isomer.

While the non-ozone data follow typical LTC and NTC behavior, as described in the previous section and consistent with earlier work, (80) changes in the reactivity upon ozone addition are visible. Additional fuel consumption is observed in the temperature region around 500 K and below the LTC range, with further evidence of this increased reactivity seen in the increased production of H₂O, CO, CO₂, CH₂O, and C₂H₄O.

Furthermore, in the NTC region (starting at ∼700 K) conventionally characterized by decreased reactivity as observed for the non-ozone case, an increased reactivity is instead seen for the ozone case, with both increased fuel consumption and increased production of intermediates and products. A similar increased reactivity in the NTC region has been observed in previous ozonolysis experiments of ethylene. (72) It is noteworthy, however, that, for the depicted species, the mole fractions in the LTC region are similar for the ozone and the non-ozone cases.

It is also interesting to note that this increased reactivity causes slightly more incomplete combustion in the intermediate regime, as there is an appreciably lower concentration of CO₂ and a corresponding increase of CO at temperatures near 900 K, as well as some formation of CH₂O that is not present in the non-ozone data. The second peak in the intermediate temperature range is less pronounced in the ozone case than in the non-ozone case. This observation is, possibly, evidence that CH₂O is being consumed at temperatures lower than traditional intermediate chemistry.

While it is beyond the scope of the present work to discuss the many species-specific mole fraction profiles available, some general trends are discussed. The rest of the full set of experimental data is available in the Supporting Information. For example, smaller hydrocarbon fragments, such as C₃H₆ and C₄H₆ seen in Figure 10a,b, show an uptick in concentration in the NTC regime, driven by the increased fuel consumption. The observed signal intensities at the maximum recorded temperature indicate that these species appear in higher concentrations than in the non-ozone experiments.

Figure 10

Figure 10. Signal intensities as a function of temperature for both the ozone (□) and non-ozone (○) cases for (a) C₃H₆, (b) C₄H₆, (c) C₄H₄O, (d) C₃H₆O, and (e) CH₂O₂.

Signals corresponding to C₄H₄O and C₃H₆O species (please note that a detailed identification of the isomeric contributions is beyond the scope of the present work) show similar temperature peak behaviors in both the ozone and the non-ozone cases as CH₂O and C₂H₄O. That is, there is an increased formation of these species observed in the temperature region below the LTC regime, while in the NTC regime concentrations are more of a flat background, with no clear peaks compared to the peaks seen in the non-ozone data. For C₃H₆O, the effect on the NTC regime is less pronounced, while a big effect can be seen at temperatures below LTC. As for CH₂O, the signal peak of C₃H₆O near 900 K is less pronounced in the ozone case, probably indicating an increased oxidation rate. And then there are species that are only affected in the temperature regime below the LTC range. As an example, we show the CH₂O₂ case (as shown above, identified as formic acid), in Figure 10e. Clearly a double-peak behavior is visible, while ozone addition has no effect on the CH₂O₂ profile in the NTC regime.

In summary, several trends of the temperature-dependent and molecule-specific profiles are present upon ozone addition. While in the LTC temperature range, there is little change for many of the traditional LTC species upon the addition of ozone, effects are visible either at temperatures below and/or above the LTC regime. As discussed in earlier work, (72) the reducing effect of ozone addition on the NTC regime and the formation of oxygen-containing intermediates from 700 to 1000 K is likely to be related to additional O atom chemistry. That is, in this temperature regime, the O atoms will accelerate the oxidation of the MHX radical and the respective intermediates to eventually form CO, CO₂, and H₂O.

For a complete chemical understanding and analysis, chemically detailed modeling of this process would need to be performed, which, at present, is difficult, as many of the fundamental reaction rates for large reactants are unknown (or only known with large uncertainties) at the temperatures relevant for the present work. Our assumptions about the O atom chemistry are consistent with work from Liao et al., (54) who investigated the influence of ozone addition on the oxidative reaction network of dimethyl ether and showed a significant increase in O atom concentrations in the temperature range above 700 K.

The behavior in the temperature range below the LTC is discussed in detail in the next section.

Ozone-Assisted Extreme Low-Temperature Chemistry (ELTC)

Finally, we discuss the new peaks seen at temperatures below the LTC regime in the presence of ozone, which we named the ELTC zone. Concerning the origin of the reactivity in the ELTC regime: MHX contains no C═C double bond, and therefore ozonolysis-type processes are not expected. MHX does contain a C═O double bond, but its reactivity with O₃ is unknown, and this chemistry is not considered here. Initiation via abstraction by O₃ leading to the reactant radical species + OH + O₂ is likely slow.

Instead, noting that the observed peaks correlate with the thermal decomposition of O₃ (R11), we attribute the ELTC chemistry to reaction with O atoms, as discussed next and in Section 6. In the absence of any reactant, ozone fully thermally decomposes at 450 K. With the O₃ model from refs (53,72,and73), ozone depletion in the absence of other reactants and the modeled atomic O concentration are shown in Figure 11. The experimental O₃ concentration seen in this study is shown by the dotted line. It is clear from this figure that the O₃ concentration is already falling by the first experimental data point, and immediately afterward the ozone concentration drastically drops. Approximately 80% of O₃ is decomposed and consumed near the peak in the reactivity of the ELTC region. Interactions of the reactant MHX with ozone clearly accelerate its consumption relative to just its thermal decomposition. Simultaneously, the model predicts that the atomic O concentration rises due to this thermal decomposition, and this feature matches both the rise and fall of the ELTC region almost perfectly, as indicated by the CH₄O₂ and C₂H₄O₂ concentrations, species often used as LTC indicators. The dashed red line is the CH₄O₂ signal from the non-ozone case. This additional ELTC peak, as seen throughout the figures in this paper, is entirely absent in experiments without ozone addition. The agreement of these features with the peak O atom concentration suggests that the ELTC chemistry here is due to radical reactions initiated by O atoms originating from O₃ thermal decomposition:

(R12)

The reaction (R12) is likely to be faster than O atom addition to the C═O double bond in the ester function of MHX. This is supported by the low signal intensities in the ELTC region of the expected decomposition products of such an O+MHX adduct.

Keep in mind that the O atom profile shown in Figure 11 is based on the O₃/O₂/Ar system, in the absence of the reactant. Under these conditions the

(R13)

reaction leads to the predicted depletion of the O atoms at higher temperatures. However, in the presence of MHX, reaction (R13) becomes competitive to reaction (R12) and other reactions of O atoms [from reaction (R11)] with MHX and other oxidation intermediates, including the MHX radical.

Consistent with the picture that the ELTC chemistry is triggered by O-atom-initiated H abstraction of MHX (R12), the O₂-addtion and -isomerization reactions, which are typical for the LTC, can occur. Not surprisingly, the profiles of the typical LTC species (as shown in Figure 8) are majorly affected by the O₃ addition, and the respective temperature profiles upon addition of ozone to the MHX/O₂ mixture are shown in Figure 12. Although reaction (R12) provides access to reactive OH radicals that serve as chain carriers in the LTC regime, the temperature-dependent profiles of the hydroperoxide species (including the keto-hydroperoxide) in Figure 12 reveal some interesting differences of the chemistries in the ELTC and LTC regime. After initiation via reaction (R12), the peroxide chemistry in (R2–R7) is activated, and hydroperoxides accumulate in concentrations much higher than in the LTC region. This suggests that temperatures are not sufficient for the keto-hydroperoxide [O═POOH in (R6)] to dissociate to promote chain branching as in the typical LTC regime.

Figure 12

Figure 12. Temperature profiles of (a) KHPs, (b) olefinic hydroperoxides, diketones, ketones/cyclic ethers, and hydroperoxides, (c) methyl hydroperoxide, and (d) hydroxy-methyl hexanoate upon addition of ozone to the MHX/O₂ mixture (solid line + symbols). To guide the readers’ eyes, we included non-ozone profiles for (a) the KHP, (b) the olefinic hydroperoxide, (c) methyl hydroperoxide, and (d) the hydroxy-methyl hexanoate.

The observed temperature profiles are consistent with chain-propagating reactions R13–(R15)

(R13A)

(R14)

(R15)

which indicate that, when the source of OH (R12) or O₃ depletes, the chain-propagating reactions come to an end.

These findings are consistent with the chemical networks discussed by Liao et al. on the interaction of dimethyl ether with ozone. (54) In their work, the observed broadening of the LTC regime is explained by modeling work, indicating that the RO₂· chemistry is changing over a relatively small temperature range from 400 to 480 K. Rather than isomerization of the RO₂· to ·QOOH (R3), the recombination reaction R16 and the disproportination reaction R17 become favorable.

(R16)

(R17)

The products of reaction R17 are observed in the ELTC regime in significant amounts as shown in Figure 12d. Possible R′O and ROH structures include CH₃(CH₂)₃C(═O)C(═O)OCH₃ and CH₃(CH₂)₃CH(OH)C(═O)OCH₃, respectively, but other isomers cannot be excluded.

Furthermore, there is compelling evidence that the chemistries in the ELTC and LTC regions are exhibiting slightly different pathways. Not only are species profiles different but there is also some evidence that the isomers being formed are also unique. Figure 13 shows the temperature-dependent profiles of two sets of species at different photoionization energies: CH₄O₂ and C₇H₁₀O₅ at 10 and 11.5 eV and C₄H₈O and C₆H₈O₂ at 9.5 and 11 eV. CH₄O₂ and C₇H₁₀O₅ have excellent agreement between the two photon energies and between the ELTC and LTC regimes, suggesting that the species formed in the different temperature regions are likely the same isomer(s). Nevertheless, it should be pointed out that, as seen already in Figures 10–12, the intensities vary between the two distinct temperature regions, thus indicating differences in the ongoing chemistry. Furthermore, looking at Figure 13b, different trends for the ELTC and LTC regimes can be seen in the C₄H₈O and C₆H₈O₂ profiles. Notably, the two sets of profiles have opposite trends. That is, while the signal increases for C₄H₈O at 11.0 eV for the LTC region, the signal for C₆H₈O₂ is more pronounced in the ELTC region at the higher photon energy. The reason for this observation is not entirely clear. These differences may arise from the more (or less) pronounced accumulation of the C₄H₈O and C₆H₈O₂ isomers in the ELTC and LTC regions or from more (or less) pronounced dissociative ionization processes. In any case, these differences indicate different chemical compositions of the gases sampled at different temperatures. Specifically, one possible explanation is the production of different isomeric forms with ionization energies above 9.5 eV and that only become detectable at the higher photon energy. These features of the 9.5 and 11.0 eV temperature-profile scans suggest different chemistries at the respective ELTC and the LTC temperatures. Additional experimental and modeling work would be needed to elucidate the different chemical pathways.

Figure 13

Figure 13. Temperature profiles of (a) CH₄O₂ and C₇H₁₀O₅ at 10.0 and 11.5 eV and (b) C₄H₈O and C₆H₈O₂ at 9.5 and 11.0 eV. See text for details.

Most importantly, the change in species behavior demonstrates that this ELTC regime cannot be viewed as just an extension of the LTC behavior but instead as its own regime with competing reaction pathways that again cause an NTC behavior between the ELTC and LTC behaviors. Modeling efforts are required to determine the important pathways governing this regime, and this chemistry merits further study.

To summarize, our experimental results indicate that, in the ELTC region, the O + MHX reaction (R12) is dominant, but the chain-branching reactions, typically observed in the low-temperature chemistry regime, are slow at these temperatures. Because of these extreme low temperatures, some species, that is, the hydroperoxides and keto-hydroperoxides, form in larger amounts typically not observed in the LTC. The lower temperature leads to a slightly different observed chemistry; that is, the disproportination reaction (R17) becomes more important. As the temperature rises, reaction (R13) becomes faster, slowing the fuel decomposition so overall reactivity decreases. In the LTC region, the temperatures are high enough to promote chain branching and QOOH decomposition, and then in the NTC region we have increasing reactivity with intermediates as well leading to product species formation.

Theory

As discussed above, the experimental results in Section 5 demonstrate that ozone decomposition promotes MHX initiation reactions at temperatures as low as ∼450 K, which is ∼100 K lower than this reactant’s conventional LTC chemistry regime. This result can be contrasted with the earlier, similar study of dimethyl ether, (54) where enhanced reactivity at temperatures below the LTC regime was not observed. In this section, we provide a set of computed rate constants in support of these experimental observations.

In the presence of ozone and at temperatures high enough (>450 K) at which ozone decomposes to O + O₂ (R10), initiation is assumed to occur via O atom abstraction reactions R11. Rate constants for (R11) have been measured for DME (103,104) and calculated recently for a methyl ester smaller than the one of interest here, methyl propanoate (MPR). (105) According to these literature values, k_DME+O ≈ 10k_MPR+O at ∼500 K, which would suggest that MPR is less likely to be initiated via O₃ decomposition than DME. The present experimental interpretation requires this trend be reversed for the larger methyl ester of interest here, MHX; that is, that k_DME+O ≪ k_MHX+O at ∼500 K.

Hydrogen atom abstraction rate constants are generally expected to increase with fuel size as the number of available H atoms grows. These increases can indeed be significant (several orders of magnitude) at low temperatures for small species, where the relative fractions of primary, secondary, and tertiary H atoms change significantly with size. For systems with more than a few heavy atoms, however, rate constants are more likely to increase approximately linearly as CH₂ units are added. To better motivate the present experimental interpretation, ab initio rate constants (106,107) for (R11) were calculated for DME and the series of four methyl esters: MPR, methyl butanoate (MB), methyl pentanoate (MPE), and MHX.

Sensitivity to the level of electronic structure theory was first quantified. Two low-level methods (M06-2X and B2PLYP-D3, both using the TZ = cc-pVTZ basis set) and three dual-level approaches with CCSD(T)-F12-based energies were tested, as summarized in Table 1 for a single abstraction barrier height for each reactant, namely, the α-H atom from the linear methyl ester conformer, where the α-H atom is bonded to the C atom closest to the ester group along the alkyl chain. For MXH, this abstraction reaction produces the fuel radical R depicted in Figure 7. Notably, despite the large deviations in the two low-level energies, the two dual level CCSD(T)-F12/CBS energies (where the CBS limit is based on a two-point extrapolation and cc-pVDZ and cc-pVTZ basis sets) are in close agreement with one another, differing by just ∼0.15 kcal/mol.

Table 1. Calculated α-H Abstraction Barrier Heightsa

reaction	I = M06-2X/TZ	II = B2PYLP-D3/TZ	CCSD(T)-F12/DZ-12//I	CCSD(T)-F12/CBS//I	CCSD(T)-F12/CBS//II
DME+O	0.77	8.31	5.36	5.19 (4.28)b	5.32 (4.57)
MPR+Oc	3.85	11.20	7.90	7.54 (7.15)	7.69
MB+O	0.77	7.83	4.79	4.32 (3.70)	4.48
MPE+O	0.95	7.93	5.05	4.57 (2.71)	4.68
MHX+O	0.98	8.02	5.09	4.59 (2.86)	4.78

^a

Calculated α-H abstraction barrier heights from linear fuel conformers (kcal/mol).^b

The effect of including anharmonic ZPE corrections computed using the relevant DFT method is shown in parentheses.^c

This saddle-point energy was previously calculated to be 6.6 and 8.4 kcal/mol at the CCSD(T)/CBS//M08-HX/cc-pVTZ and MRSDCI+DS/CBS//M08-HX/cc-pVTZ levels of theory, respectively. (105)

The results reported below were typically obtained using CCSD(T)-F12/CBS//M06-2X/TZ, which is less computationally demanding than CCSD(T)-F12/CBS//B2PYLP-D3/TZ. In some cases, we used the even less expensive CCSD(T)-F12/DZ-12//M06-2X/TZ approach, which, as shown in Table 1, differs from the more accurate calculations by ∼0.4 kcal/mol. We did not use CCSD(T)-F12/DZ-12//M06-2X/TZ for absolute barrier heights, however. Instead, this level of theory was used for MHX to compute the energies of nearly 100 saddle points for several conformers and H atom abstraction sites relative to the energy of the lowest-energy one. When used in this way, the CCSD(T)-F12/DZ-12//M06-2X/TZ method was found to differ from the more expensive CCSD(T)-F12/CBS//M06-2X/TZ approach by just ∼0.1 kcal/mol, on average, using all of the saddle points for MB + O as a test case.

Table 1 includes the results of anharmonic zero-point energy (ZPE) corrections, which were calculated using a second-order perturbation (108) as implemented in Gaussian 16. These corrections are fairly large, much larger than the likely few tenths of a kilocalorie per mole errors in the electronic energies quantified above, varying from −0.7 kcal/mol for MPR + O to −2.5 kcal/mol for MHX + O. Corrections of this size have a significant impact on the computed rate constants at the low temperatures of interest here, for example, increasing k_MHX+O by a factor of 6 at 500 K! Clearly, this correction factor is a significant source of uncertainty in the present calculations. Improved estimates of zero-point energy corrections could perhaps be obtained, (109) but their computation would be a significant (and likely prohibitive) challenge for systems as large as MHX + O and for saddle points in general.

The complexity that arises due the presence of low-energy fuel conformers and multiple nonequivalent H-atom abstraction sites was addressed as follows. Fuel conformers were generated using the informatics tool Open Babel, (110) and their relative energies were obtained using the dual-level methods discussed above. For MPR, there are no low-energy conformers of importance, as there are none within 7 kcal/mol of the global (linear) minimum. The number of low-lying conformers grows rapidly for the larger methyl esters, however, and, notably, for methyl esters larger than MPR, we found two nearly isoenergetic conformers within 0.1 kcal/mol of each other. The linear conformer is the slightly higher-energy conformer of the pair, with the lower-energy conformer related to it via a 120° twist of the α–β C atoms. Additional low-lying conformers appear at ∼0.5 kcal/mol above these lowest-energy ones. To provide a sense of the scope of the problem, we note that our procedure found 4, 11, and 21 conformers with energies within 2 kcal/mol of the lowest-energy ones for MB, MPE, and MHX, respectively. Only the linear conformers have symmetry, and so each conformer requires, generally, the characterization of 10, 12, and 14 H-atom abstraction saddle points for MB + O, MPE + O, and MHX + O, respectively, for a total of 36, 127, and 288 saddle points for these three systems.

Rate constants were calculated using the following approach designed to deal with this combinatorial complexity. The rigid rotor/harmonic oscillator (RRHO) approximation was used to compute a single conformer- and site-specific rate constant k_ij for the lowest-energy (linear) conformer (i = 1) and for the α-H abstraction site (j = 1). The computed rate constant was multiplied by 1 + exp(−ΔE/k_BT) to account for the first-excited electronic state, where ΔE is the estimated energy gap of the two electronic states at the reference saddle point. For O atom abstraction reactions, ΔE is typically small, and this expression is close to 2, even at low temperatures. For CH₄ + O, for example, the difference in the saddle point energies for the two lowest-energy states is just 0.2 kcal/mol. We confirmed the smallness of this energy difference for DME + O, which we computed to be 0.43 kcal/mol at the CAS(3o,4e)PT2/aug-cc-pVTZ level of theory. For the methyl esters, we estimated ΔE = 0.3 kcal/mol.

The total rate constant was approximated

(E1)

where f_C is a simple correction factor to account for the multiple abstraction sites and conformers.(E2)

Here, g_ij and V_ij^‡ are the degeneracy factor and energy of the ijth saddle point, and E_i is the energy of the ith conformer. Equation E2 relies on the simplifying assumption that entropic and tunneling contributions to the rate constant are less sensitive to the fuel conformer and/or abstraction site relative to the energetic contribution. The accuracy of this assumption is dependent on how representative the lowest-energy saddle point is of the rest of them, and it could be improved by replacing k₁₁ with some ensemble average of k_ij for a few saddle points to make it more representative. Such an approach is not tested here.

One might prefer a calculation where one-dimensional hindered rotors (1DHRs) are used. Such an approach is tested here, but only for the two smallest systems DME + O (calculated as part of this work) and MPR + O (taken from ref (105)). As shown below, we find very small differences between the RRHO and 1DHR results for these two systems. 1DHR results are generally assumed to be more accurate, but we caution against this assumption for large systems, where the scaling of the accuracy of 1DHR approaches is not well-understood. In our own recent studies comparing fully coupled and fully anharmonic Monte Carlo phase space integral partition functions (111) with RRHO, separable 1DHR, and multidimensional HR models, we found that the error in the partition function using a 1DHR model increased from just 20%, on average, for systems with one fluxional mode (such as a torsion) to factors of 2 and 7 for systems with two and three fluxional modes, respectively. (112,113) These errors are in fact comparable in magnitude to those quantified in the same study for a single conformer RRHO model. (Note that E1 and E2 improve on the single conformer RRHO model by including the effects of multiple conformers, but such a multiconformer RRHO method was not tested in ref (113).) It is unknown how well conclusions drawn for stable species can be applied to the description of transition states, but we can say that it is generally more difficult to define and separate torsions for transition states (which necessarily have a variety of low-frequency motions, many of which cannot be straightforwardly described as torsions) than for stable species. Rate constants are proportional to the ratio of the pseudopartition function for the transition state to the partition function for the reactants, and so one expects some cancellation of these rather large anharmonic effects. The degree of cancellation is largely unknown, and anharmonicity is unavoidably a considerable source of uncertainty in rate constant calculations for large systems. Altogether these considerations suggest that 1DHR models should not necessarily be expected to be substantively more accurate than the simple multiconformer RRHO model described in equations E1 and E2 for large systems, despite the significant additional computational complexity that HR models require. Equations E1 and E2, in contrast, are readily implemented. For the H-atom abstraction reactions considered here, we found we could trivially automate the generation of guessed geometries and the dual-level quantum chemistry optimizations and calculations required for the evaluation of f_C in eq E2.

The results of eq E1 for DME + O and four methyl esters + O are shown in Figure 14. The computed rate constants for DME + O and MPR + O are shown to agree quantitatively with those computed using separable 1DHR models, as noted above. The computed rate constant for DME + O is just half as large as the experimentally determined expression from ref (103) at 300 K, and this difference is close to the assigned experimental uncertainty. Agreement improves with increasing temperature, and the calculated and experimental values agree very closely at 450 K. Likewise, the present calculation at 1000 K (7.5 × 10^–12 cm³ molecule^–1 s^–1) agrees quantitatively with the experimental measurement of ref (104) (1.1 × 10^–11 cm³ molecule^–1 s^–1, with an error bar of a factor of ∼5). Altogether these comparisons are quite favorable for eq E1, although we again draw attention to the significant sources of error in these calculations (principally associated with anharmonicity, as discussed above) that suggest that its quantitative performance is at least somewhat fortuitous.

Figure 14

Figure 14. Calculated total rate constants for O + DME and O + four methyl esters (MHX = methyl hexanoate, MPE = methyl pentanoate, MB = methyl butanoate, MPR = methyl propanoate). The present results (solid lines) are compared with the 1DHR calculations (dashed lines) for DME (present work) and MPR (taken from ref (101)) and with an experimentally derived Arrhenius expression (99) (●) for DME.

Here we are principally interested in trends in the rate constants for the series of methyl esters and DME at ∼500 K. We find that the rate constant at 500 K increases by nearly an order of magnitude going from MPR + O to MB + O (k_MB+O/k_MPR+O = 8.4), with relative increases that continue but diminish with size (k_MPE+O/k_MB+O = 5.2 and k_MHX+O/k_MPE+O = 2.1), as may be expected.

The relative changes in k₁₁ for this series are straightforwardly rationalized by the trends in the Botlzmann-weighted barrier heights given in Table 1. Trends in f_C are somewhat more complex. At 500 K, for example, f_C = 2.1, 0.6, 1.7, and 2.7 for MPR, MB, MPE, and MHX, respectively. For MPR+O, only one conformer contributes to k, and f_C thus represents the increase in the total rate constant due to the presence of additional H-atom abstraction sites. Each additional nonequivalent abstraction site increases the total rate by 20–40% at 500 K relative to k₁₁ (for the two equivalent α-H atom abstractions), leading overall to a doubling of the total rate constant relative to k₁₁.

For MB+O, four low-energy conformers were found and included in f_C: two with nearly degenerate energies and two with energies just ∼0.6 higher. For this system, the barrier height for the reference saddle point (abstraction from the α-site on the linear conformer) is substantially lower in energy than the saddle-point energies for the other conformers and abstraction sites, such that collectively the effect the other 31 saddle points for MB + O is quite small, with the numerator of f_C evaluating to just 1.9 at 500 K. The denominator, in contrast, is close to 3, thus resulting in f_C < 1 and a reduction in the total rate constant relative to k₁₁. Physically, this situation corresponds to reactant population getting stuck in less-reactive conformers.

MPE + O is not discussed in detail and is similar to MHX + O. In contrast to MB + O, several conformers of MHX have low-energy saddle points for abstraction within a few tenths of a kilocalorie per mole of that of the reference saddle point for α-H atom abstraction from the linear conformer. In fact, all of the 20 conformers considered contributed non-negligibly to f_C, even at temperatures as low as 500 K. In principle, then, it is necessary to consider additional higher-energy conformers until their energies become high enough that these conformers stop contributing to f_C. This is likely not necessary, however, as we note that contributions to f_C from just the two lowest-energy conformers (with nearly degenerate conformer energies) are 3.5 and 2.1, which average to ∼2.8 in close agreement with the overall f_C. As additional conformers are added one by one, the Boltzmann-averaged correction f_C remains close to ∼2.7, suggesting that f_C converges much more rapidly than requiring that the highest-energy terms in the numerator and denominator go to zero.

To conclude this section, we note that the present results support the experimental observation that ozone decomposition promotes initiation around 500 K ∼10 times more strongly for MHX than for DME. More generally, we can further speculate that H-abstraction initiation reactions by O atoms are likely to be more sensitive to fuel structure than conventional initiation via abstraction by O₂. Rate constants for abstraction by O₂ are typically small due to these reactions’ late, large barriers, and fuel-dependent variations in these barriers of a few kilocalories per mole amount to relatively small changes in the forward barrier heights.

Conclusion

The accelerating effect of ozone on the oxidation of methyl hexanoate was investigated over a temperature range from 460 to 940 K. Using a jet-stirred reactor and molecular beam mass spectrometer we probed the identity and the temperature profiles of key intermediates. In the absence of ozone, the typical LTC and NTC behaviors were observed in the respective temperature ranges. Upon ozone addition we observed the following.

In the LTC region, no differences were observed in the species profiles apart from slight changes in concentration. Overall, our results demonstrate little change on the LTC pathways. This may be because the ozone decomposition time scale is longer or comparable with the LTC time scale. However, because of the formation of O atoms via the thermal decomposition of ozone in this temperature range, contributions of the O atoms toward the reactant’s radical formation are expected, in addition to the typical H abstraction via OH radicals.

At higher NTC temperatures, at which the time scale of ozone decomposition was significantly decreased, drastic differences were seen in major product species such as H₂O, CO, and CO₂, with a large rise in concentration around 700 K. Oxygenated intermediates, such as acetaldehyde and formaldehyde, showed several other trends, either increased reactivity in the NTC regime followed by a traditional intermediate temperature peak or just a flat background of reactivity. In this temperature range, the O₃ decomposition is known to be fast, leading to O atoms and their respective reactions with MHX, MHX radicals, and other oxidation intermediates becoming important compared to O-atom recombination reactions. Nevertheless, modeling efforts will need to be conducted to understand these shifting pathways.

Finally, a new regime was observed, dubbed the extreme low-temperature chemistry, at temperatures below traditional LTC. In this ELTC range, the ozone decomposition time scale is long compared to that of the LTC and NTC regions but shorter than the time scale of the peroxide chemistry in the ELTC region. As a result, it was found that ozone thermal decomposition and the production of O atoms boosted reactivity at these low temperatures. Our theoretical calculations suggest that ozone-assisted initiation in the ELTC regime occurring via H atom abstraction by O atoms may be more sensitive to fuel structure than conventional O₂/OH initiation. The theoretical rate constants were shown to increase rapidly with the fuel molecule size, due in part to the effects of low-lying fuel conformers and multiple abstraction sites. Notably, we found that the rate constant for DME + O was an order of magnitude slower than that for MHX + O around 500 K, which helps explain why the ELTC regime observed here for MHX + O was not observed in a similar JSR study of DME. (54) Our results indicate that, following the initiation reaction (H-atom abstraction via O atoms) and MHX radical formation, the LTC-like peroxide chemistry dominates the ELTC regime as well. The similarity in species identities suggest that the system behaves similarly in both temperature ranges. However, the observed increase in KHP (and other peroxide species) concentrations suggests that the temperatures are too low, and the LTC-like chemistry is too slow to be self-sustaining. The observed differences in concentrations and the detection of distinct isomers present at different photon energies in either LTC or ELTC regimes indicate that competing chemical pathways are active. The experimental data suggest that the chemistry of the radicals O, OH, HO₂ and their reactions with ozone, reactant, and other intermediates needs further attention. Modeling tools such as reaction path and sensitivity analysis using a validated chemical mechanism will be necessary to answer some of the remaining questions. Our observations merit further study through the use of modeling and additional experimentation.