Thermochemical and Chemical Kinetic Data
for Fluorinated Hydrocarbons
D.R.F Burgess, Jr., M.R. Zachariah, W. Tsang
Chemical Science and Technology Laboratory
National Institute of Standards and Technology
Gaithersburg, MD 20899-0001
and
P.R. Westmoreland
Department of Chemical Engineering
University of Massachusetts
Amherst, MA 01003-3110
ABSTRACT
A comprehensive, detailed chemical kinetic mechanism was developed and is presented for C1 and C2 fluorinated hydrocarbon destruction and flame suppression. Existing fluorinated hydrocarbon thermochemistry and kinetics were compiled from the literature and evaluated. For species where no or incomplete thermochemistry was available, these data were calculated through application of ab initio molecular orbital theory. Group additivity values were determined consistent with experimental and ab initio data. For reactions where no or limited kinetics was available, these data were estimated by analogy to hydrocarbon reactions, by using empirical relationships from other fluorinated hydrocarbon reactions, by ab initio transition state calculations, and by application of RRKM and QRRK methods. The chemistry was modeled considering different transport conditions (plug flow, premixed flame, opposed flow diffusion flame) and using different fuels (methane, ethylene), equivalence ratios, agents (fluoromethanes, fluoroethanes) and agent concentrations. This report provides a compilation and analysis of the thermochemical and chemical kinetic data used in this work.
3. Reaction Kinetics
3.1. Overview
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The reaction set or "mechanism" is too large to be described in detail here and, consequently, only an overview of important classes of reactions will be presented. Utilizing the species identified as potentially important, a grid of possible reactions was constructed. Existing chemical rate data involving these fluorinated species was then compiled and evaluated. Where rate data were available, but only over limited temperature ranges or at different pressures (for unimolecular or chemically activated steps), RRKM (Robinson and Holbrook, 1972) and QRRK (Dean and Westmoreland, 1987) analysis were used to estimate the temperature dependencies (at 1 atmosphere) of the rates and to predict relative rates where multiple product channels were possible. Where no rate data were available for potential reactions, the rate constants were estimated by analogy to other hydrocarbon or substituted hydrocarbon reactions. The prefactors were adjusted for reaction path degeneracy and the activation energies were adjusted empirically based on relative heats of reaction or relative bond energies (i.e., Evans-Polanyi relationships).
Initially, upper limits were used for estimated rate constants. If as a result of simulations under a variety of conditions (using different agents, flame geometries, etc.), it was observed that a specific reaction with an upper limit rate constant did not significantly contribute to the destruction or creation of any of the species in the "mechanism," then that estimate was continued to be used. However, if a specific reaction contributed to the chemistry and its rate constant was an upper-limit estimate, then its value was reevaluated and possibly refined. For important contributing reactions where no good analogy was available, where significant uncertainty existed in the barrier (generally reactions with tight transition states and modest-to-large barriers), or where multiple, energetically similar product channels were possible, we calculated the geometries and energies of the transition states (Zachariah et al., 1995) using the BAC-MP4 ab initio method. RRKM analysis was then used to obtain the temperature (and pressure) dependence of the rate constant. A brief description of the RRKM/Master Equation approach and BAC-MP4 transition state calculations used in this work are given in Section 3.5 and Section 3.6, respectively.
A listing of the rate constants in the reaction set or mechanism used in the simulations is given below in Table 5. In addition, other reactions were also considered but were observed not to contribute under the conditions tested. Many of the relevant rate constants can be found in the "NIST Chemical Kinetics Database" (Mallard et al., 1995). All references for kinetic data can be found in the relevant sections of the Bibliography: Section 6.2. General Thermochemistry and Kinetics, Section 6.7. Fluorocarbon Kinetics (decompositions), Section 6.8. Fluorocarbon Kinetics (abstractions), Section 6.9. Fluorocarbon Kinetics (oxidations), Section 6.10. Oxidized Fluorocarbon Kinetics, and Section 6.11. Fluorocarbon Kinetics (other).
A qualitative discussion of the uncertainties in the rate expressions is provided with each class of reaction. For rate expressions traceable to experimental measurements, quantitative evaluation of the uncertainties can be found in the original sources.
A schematic of the possible reaction pathways for the fluorinated hydrocarbon mechanism is given in Figure 1. This schematic provides no indication of the relative contributions of each of the possible reaction pathways since this is highly dependent upon conditions. Rather, this schematic gives an indication of the connectivity between all of the species and how the different types of reaction (e.g., thermal decompositions, chemically activated decompositions, abstractions, etc.) provide this connectivity between different types of species. For example, the linkages between each fluoromethane and the corresponding fluoromethylene is due to thermal decomposition and are indicated with bold solid arrows. Other thermal decompositions involving HF elimination (e.g., fluoroethanes => fluoroethylenes, CHF=O => CO) are also represented by bold solid arrows. Thermal decompositions involving H and F atom elimination are represented by plain dotted arrows. H atom addition/elimination reactions are represented by reversible plain dotted arrows (e.g., CH3-CHF* <=> CH2=CHF + H). Similarly, chemically activated decompositions, such as fluoromethyls => ["hot" fluoromethanes] => fluoromethylenes, are represented by bold dashed arrows (for reactions involving H atoms) and plain dashed arrows (for reactions involving O atoms and OH radicals). Abstraction type reactions (e.g., fluoromethanes => fluoromethyls) are represented by plain solid arrows. A few of the potential reaction pathways are not shown in Figure 1 for purposes of maintaining clarity in the schematic representation.
For any given condition (e.g., temperature, concentration) and any given fluorocarbon, only a subset of the reactions pathways will be relevant. For each reaction pathway that is possible, each will have a different relative importance. A discussion of each of the different reaction types for each species type can be found in the following sections.
3.2. Hydrocarbon and H/O/F Chemistry
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The C/H/O subset is derived from the Miller-Bowman mechanism (Miller and Bowman, 1989) and consists of about 30 species and 140 reactions (see reactions labeled "HO" and "HC" in Table 5). Any other hydrocarbon mechanism could be used instead. For example, the GRIMECH set (Bowman et al., 1995) is a recent hydrocarbon mechanism that accurately reproduces flame speeds for methane mixtures.
The H/O/F subset consists of 3 species (F, HF) and 8 reactions (reactions labeled "HF" in Table 5) that are relatively well known. This is the chemistry of fluorine atoms with hydrogen- and oxygen-containing species, such as H2, OH, and H2O. There are three reactions of this type that were determined to participate in the chemistry under a variety of conditions. These reactions are the combination of H and F to form HF (or the reverse decomposition) and the hydrogen atom transfer reactions by F atoms from H2 and H2O.
The HF decomposition reaction has been measured only at temperatures above about 4000 K (Jacobs et al., 1965; Blauer, 1968, Blauer et al., 1971). Although this reaction in the decomposition direction is unimportant at typical flame temperatures, the reverse H + F = HF combination must be considered. Extrapolating the recommended value (Baulch et al., 1981) for decomposition to 1000 K may result in an uncertainty of as much as a factor of ten, especially when considering non-simple Arrhenius dependence to the rate and different third-body efficiencies. However, since many other reactions (F + H2, H2O, RH) contribute to F atom destruction, the uncertainty in the absolute rate of the forward or reverse reaction is most likely unimportant.
The hydrogen abstraction reactions from H2 and H2O by F atoms have been measured only near room temperature (Wurzberg and Houston, 1980; Stevens et al., 1989; Walther and Wagner, 1983). These values were extended to higher temperatures by fitting the reported values to extended Arrhenius expressions (ATbe-E/RT). For the H2 reaction, an expression with T0.5 dependence was chosen consistent with the value recommended by Cohen and Westberg (1983). For the H2O reaction, an expression with T1.5 dependence was chosen by analogy to other reactions.
There are a number of other reactions which were included in the mechanism, but were never observed to contribute significantly to the chemistry. These reactions include the combination of F atoms to form F2 and the hydrogen abstractions by F atoms from OH, HO2, and H2O2. The oxy-fluoro-species FO*, HOF, FOO*, and F2O were also initially considered in the mechanism. However, given the very low concentration of F atoms at high temperatures in the hydrocarbon/air flame, these species are present in extremely low concentrations and do not contribute to the overall chemistry. The rate constants used for reactions involving these species are not given in Table 5.
3.3. C1 Fluorinated Hydrocarbon Chemistry
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3.3.1. Overview
The C1 subset of the reaction set (approximately 150 reactions) consists of chemistry of 14 species containing one carbon (and hydrogen/fluorine/oxygen) with H, O, OH, H2O, and other flame species. The C1/H/F/O species used in this reaction set are the fluoromethanes (CH3F, CH2F2, CHF3, CF4), the fluoromethyl radicals (*CH2F, *CHF2, *CF3), the fluoromethylenes (:CHF, :CF2), and the fluoromethylidyne radical (*CF). The oxidized C1 fluorocarbon species contained in this reaction set are the perfluoromethoxy radical (CF3O*) and the carbonyl fluorides (CHF=O, CF2=O, *CF=O). Other oxidized C1 fluorocarbon species were initially considered in the development of the mechanism, but later were excluded, such as the other fluoromethoxy radicals (CH2FO*, CHF2O*), the fluorohydroxymethyl radicals (*CHFOH, *CF2OH), the perfluoromethylperoxy radical (CF3OO*), and perfluoromethanol (CF3OH). Although these species (and others) may be important in atmospheric chemistry, our initial simulations suggest that they are present in extremely low concentrations at high temperatures in hydrocarbon/air flames and do not contribute to the overall chemistry.
Both thermally and chemically activated decompositions were considered (e.g., CH2F2 => :CHF + HF and *CHF2 + H => :CHF + HF). Fluoromethane decompositions via abstraction of H atoms by H, O, and OH radicals are important pathways. Fluoromethane metathesis reactions with methyl, ethyl, vinyl, and fluoromethyl radicals must also be considered. The reaction set also includes reactions of fluoromethyls with O2, O, and OH to form carbonyl fluorides (e.g., CF2=O) and other products, and reactions of the fluoromethylenes (e.g., :CF2) with H to form *CF and O2, O, or OH to form carbonyl fluorides. The carbonyl fluorides (i.e., CHF=O, CF2=O, and *CF=O) can be destroyed via unimolecular decomposition, by reactions with H atoms (both abstractions and addition/eliminations), and through reactions with OH radicals (abstractions). Destruction of CF2=O through complex formation with H2O and subsequent decompositions are also considered.
3.3.2. Fluoromethanes: Decompositions
Rate expressions for thermally and chemically activated decompositions of the fluoromethanes are labeled "MD" in Table 5.
The fluoromethanes are primarily destroyed in hydrocarbon flames via H atom abstraction by H and OH and through unimolecular decomposition. Destruction via H atom abstraction by O atoms is a minor channel. The biggest uncertainties for the destruction of the fluoromethanes are the unimolecular decompositions. Although there are reliable experimental data for these reactions, their strong temperature and pressure dependencies results in a level of uncertainty to these reactions at flame temperatures. Further mechanism refinements should provide better rate expressions for these reactions.
Both thermally and chemically activated decompositions of the fluoromethanes were considered (e.g., CHF3 => :CF2 + HF and *CHF2 + H => :CF2 + HF). There have been a number of measurements of the unimolecular decomposition of fluoromethanes (with HF elimination). We employed rate expressions for HF elimination from CH3F and CHF3 that are fits to extended Arrhenius form (ATbe-E/RT) to the experimental data of Schug and Wagner (1973) and Hidaka et al. (1991), respectively. These experimental data were obtained at different temperatures and pressures than are relevant to atmospheric flames. The experimental data were interpolated or extrapolated and fit using temperature dependencies (Tb) that were consistent with the experimental data and RRKM analysis. For HF elimination from CH2F2, we employed a rate expression from our RRKM analysis using BAC-MP4 transition state energies and geometries, although there is experimental data by Politanskii and Shevchuk (1968). For H2 elimination (minor channel) from CH3F and CH2F2, we used rate expressions from our RRKM analysis using BAC-MP4 ab initio transition states (Zachariah et al., 1995). F atom eliminations from the fluoromethanes are negligible decomposition channels, except for CF4, where it is the only possible pathway. For this reaction, we used a rate expression from our RRKM/Master Equation analysis that is referenced to the room temperature measurement of the reverse reaction (*CF3 + F) by Plumb and Ryan (1986).
There have been no measurements (to our knowledge) for reactions involving chemically activated or "hot" fluoromethanes other than room temperature measurements of the rate constant for CF3 + H => Products (e.g., Ryan and Plumb, 1984; Tsai and McFadden, 1989). In order to estimate values for these various reactions, as well as for the stabilized fluoromethane channels, we used RRKM analysis with experimental barriers (where they existed) or our BAC-MP4 ab initio transition state barriers (Zachariah et al., 1995) for insertion of :CHF and :CF2 into HF and H2 and the energetics of the reaction pathways. Although the chemically activated fluoromethane reactions are primary pathways for destruction of fluoromethyl radicals and there are no experimental rate measurements, the uncertainties in the rates are relatively small, since these are barrierless combinations.
There have been a number of measurements of the unimolecular decomposition of fluoromethanes (with HF elimination): at least two for CH3F (Politanskii and Shevchuk, 1967; Schug and Wagner, 1973), at least one for CH2F2 (Politanskii and Shevchuk, 1968), and several for CHF3 (Tschuikow-Roux, 1965; Tschuikow-Roux and Marte, 1965; Modica and LaGraff, 1966; Politanskii and Shevchuk, 1968; Biordi et al., 1978; Schug et al., 1979; Hidaka et al., 1991). In addition, there have been a number of measurements of the unimolecular decomposition of other halomethanes (eliminating HF, HCl, or HBr) such as CHF2Cl (Norton, 1957; Edwards and Small, 1964; Gozzo and Patrick, 1964; Edwards and Small, 1965; Gozzo and Patrick, 1966; Barnes et al., 1971; Kushina et al., 1972; Schug et al., 1979; Zhitnev et al., 1990; Zhitnev et al., 1991), CHF2Br (Cox and Simmons, 1971) , CHFCl2 (Kushina et al., 1972), and CHCl3 (Shilov and Sabirova, 1960; Schug et al., 1979). All of these halomethane decomposition reactions have a small-to-moderate barrier in the reverse direction (i.e., carbene insertion into HF, HCl, or HBr) of 10-40 kJ/mol. Consequently, all of the halomethane decomposition measurements are important from the point of evaluating the fluoromethane values (both experimental and calculated) for consistency. Furthermore, the barriers-to-insertion for :CHF and :CF2 in these reactions can be used as reference reactions for reactions of :CHF and :CF2 with many other important molecules where there is no or little information available (i.e., the reactions of :CHF and :CF2 with H2, H2O, CH4, C2H6, fluoromethanes, fluoromethyls, etc.).
3.3.3. Fluoromethanes: Abstraction of Hydrogen by H Atoms
Rate expressions for abstraction of hydrogen from the fluoromethanes are labeled "MA" in Table 5.
We used rate expressions that were fits to extended Arrhenius form (ATbe-E/RT) to the experimental data of Westenberg and deHaas (1975) and Ridley et al. (1972) for abstraction of hydrogen from CH3F and CH2F2, respectively. For abstraction of hydrogen from CHF3, we used a fit to data for the reverse reaction from work by Ayscough and Polanyi (1956) and Berces et al. (1972). A temperature dependence of T3.0 was used by analogy to that recommended for methane (Tsang and Hampson, 1986). The experimental data for these reactions were all obtained at intermediate temperatures (600-900 K) and, consequently, the uncertainties in extrapolation of these data to flame decomposition temperatures are most likely acceptable. However, modeling results suggest that flame speeds in CHF3 doped flames are relatively sensitive to the rate of hydrogen abstraction from CHF3. Consequently, future refinements of this mechanism should provide the best possible rate expression for this reaction that is consistent with all available experimental data.
There have been many measurements of abstraction of hydrogen from the fluoromethanes by H atoms. There have been at least four measurements for CH3F (Parsamyan et al., 1967; Hart et al., 1974; Westenberg and deHaas, 1975; Aders et al., 1975), at least two measurements for CH2F2 (Parsamyan and Nalbanddyan, 1968; Ridley et al., 1972), and a number of measurements or estimates for CHF3 (Ayscough and Polanyi, 1956; Pritchard et al., 1956; Skinner and Ringrose, 1965; Amphlett and Whittle, 1967; Arthur and Bell, 1968; Fagarash and Moin, 1968, Kibby and Weston, 1968; Berces et al., 1972; Kondratiev, 1972; Arthur et al., 1975; Arthur and Bell, 1978; Richter et al., 1994). We should note that many of the measurements or estimates for the CHF3 reactions are actually values for the reverse rate or *CF3 + H2 => CHF3 + H. Two of the citations (Kondratiev, 1972; Arthur and Bell, 1978) are evaluations of the experimental data. We have also calculated the structure and energy of each transition state for these reactions using the BAC-MP4 ab initio method. The calculated energy barriers compare well with the experimental values (Zachariah et al., 1995).
For the CH3F + H reaction, all of the workers cited above incorrectly identified the reaction as abstraction of fluorine rather than hydrogen. These workers only measured the disappearance of the reactants and simply assigned the product channel by analogy to the CH3Br + H reaction, where it is known that the halogen atom (Br) is abstracted. However, the C-F bond is much stronger than both the C-Br and C-H bonds. Consequently, for CH3F, abstraction of hydrogen is more favorable than abstraction of fluorine. Our ab initio transition state calculations (Zachariah et al., 1995) also support this conclusion, where abstraction of hydrogen from the fluoromethanes by H atoms were calculated to have barriers-to-reaction of 49.4, 40.6, and 53.6 kJ/mol for CH3F, CH2F2, and CHF3, respectively. In contrast, the calculated barriers for abstraction of fluorine were 131.4, 142.7, 168.6, and 171.1 kJ/mol for the CH3F, CH2F2, CHF3, and CF4, respectively. This is a significant difference and clearly supports assignment of abstraction of hydrogen as the dominant channel.
Richter et al. (1994) have measured the rate of abstraction of hydrogen from CHF3 by H atoms in H2/O2 premixed flames and report an activation energy of about 73 kJ/mol. This barrier would appear to be inconsistent with and significantly higher than values of 40-50 kJ/mol that are typical for abstraction of hydrogen by H atoms from hydrocarbons (e.g., CH4, C2H6) and other fluoromethanes (see references above).
3.3.4. Fluoromethanes: Abstraction of Hydrogen by O Atoms and OH Radicals
Rate expressions for abstraction of hydrogen from the fluoromethanes are labeled "MA" in Table 5.
In this work, for abstraction of hydrogen from the fluoromethanes by O atoms, we fit experimental data for CH3F (Parsamyan et al., 1967), CH2F2 (Parsamyan and Nalbandyan, 1968), and CHF3 (Jourdain et al., 1978) to extended Arrhenius form (ATbe-E/RT) using a temperature dependence (T1.5) by analogy to methane (Tsang and Hampson, 1986). For abstraction of hydrogen from the fluoromethanes by OH radicals, we used rate expressions as recommended by Cohen and Benson (1987) that have temperature dependencies based on transition state theory. These recommendations are based on experimental measurements at relatively low temperatures (about 300-500 K). Since these reactions are primary decomposition pathways for the fluoromethanes, it would be valuable to have experimental measurements of these rates at higher temperatures (closer to flame conditions).
There have been many measurements for abstraction of hydrogen from the fluoromethanes by H atoms, but only a few for abstraction of hydrogen by O atoms or OH radicals. Parsamyan and coworkers have measured the rate of reaction for CH3F + O (Parsamyan et al., 1967) and for CH2F2 + O (Parsamyan and Nalbandyan, 1968). Jourdain et al. (1978) and Miyoshi et al. (1993) have measured the rate of reaction for CHF3 + O. We have not used the more recent value by Miyoshi et al. (1993), because it appears that these data may be complicated by the CHF3 => :CF2 + HF decomposition reaction at the highest temperatures. This should be further examined. Richter et al. (1994) have measured the rate of H atom abstraction from CHF3 by O in H2/O2 premixed flames and report an activation energy of about 13 kJ/mol. This barrier would appear to be inconsistent with and significantly lower than typical values of 35-40 kJ/mol for H atom abstraction by O from hydrocarbons (e.g., CH4, C2H6) and other fluoromethanes (see references above).
As indicated above, Cohen and Benson (1987) used transition-state theory calculations to analyze and predict rate coefficients for reaction of OH radicals in a series of halogen-substituted methanes and ethanes. Much of their analysis is based on the experimental data of Jeong and Kaufman (1982), but it is also consistent with other measurements for fluoromethanes (Howard and Evenson, 1976; Clyne and Holt, 1979; Nip et al., 1979; Talukdar et al., 1991).
3.3.5. Fluoromethanes: Abstraction of Hydrogen by F Atoms and Fluorine by H Atoms
Rate expressions for abstraction of hydrogen by F atoms are labeled "CF" in Table 5. Rate expressions for abstraction of fluorine by H atoms are labeled "MA" in Table 5.
There have been a number of measurements of abstraction of hydrogen from methane (CH4) by F atoms near room temperature (Wagner et al., 1971; Pollock and Jones, 1973; Williams and Rowland, 1973; Manning et al., 1975; Smith et al., 1977; Clyne and Hodgson, 1983; Pagsberg et al., 1988). In our work, we used a fit to extended Arrhenius form (ATbe-E/RT) to the rate constant of recommended by Atkinson et al. (1992) using a temperature dependence (T0.5) in order to extend the rate expression to flame temperatures. Although there is some uncertainty here in extrapolating the rate constant to flame temperatures, it is most likely unimportant. This is because this reaction occurs on almost every collision (that is, the rate cannot change by much). Furthermore, there are many other reactions (e.g., F + H2, F + H2O, and F + other hydrocarbons) that contribute to F atom destruction.
For completeness in the reaction set (although it is unlikely that they will contribute), we have also included abstraction of hydrogen from the fluoromethanes by F atoms. There have been a number of measurements for these reactions near room temperature for CH3F (Pollock and Jones, 1973; Smith et al., 1977; Manocha et al., 1983), for CH2F2 (Pollock and Jones, 1973; Smith et al., 1977; Manocha et al., 1983, Clyne and Hodgson, 1985; Nielsen et al., 1992), and for CHF3 (Pollock and Jones, 1973; Goldberg and Schneider, 1976; Smith et al., 1977; Clyne and Hodgson, 1983; Maricq and Szente, 1992). For these reactions, rate expressions were used where the rate constant prefactor relative to that recommended by Atkinson et al., 1992) for CH4 + F was adjusted to account for reaction path degeneracy (i.e., fewer number of H atoms) and the activation energy was adjusted such that the rate was consistent with the measurements at room temperature. Use of extended Arrhenius form in these cases is not justified, because of the lack of temperature-dependent experimental measurements.
For abstraction of fluorine from CH3F, CH2F2, and CHF3 by H atoms, we employed rate expressions derived from our BAC-MP4 ab initio transition state calculations (Zachariah et al., 1995). These pathways are negligible channels for fluoromethane destruction and were included simply for completeness in development of the reaction set. However, for reaction of H atoms with CF4, the only possible pathway is abstraction of fluorine. For this reaction, we used the experimentally derived rate expression of Kochubei and Moin (1969, 1971). This reaction is important pathway for CF4 destruction, competing with the only other possible channel - unimolecular decomposition of CF4 to *CF3 and F.
3.3.6. Fluoromethanes: Metathetical Reactions
Rate expressions for metathetical reactions of the fluoromethanes are labeled "MA" in Table 5.
There have been a number of measurements of metathetical reactions of methyl/fluoromethyl radicals with methane/fluoromethanes. These will not be reviewed here. In our work, we used the recommendations of Kerr and Parsonage (1976), which are consistent with the majority of the experimental data. The values recommended by Kerr and Parsonage are largely based on the pioneering work in this area by Pritchard and coworkers (e.g., Pritchard et al., 1965), Whittle and coworkers (e.g., Chamberlain and Whittle, 1972), and Arthur and coworkers (e.g., Arthur and Bell, 1978).
Although there have been no experimental measurements of metathetical reactions of vinyl radicals (C2H3) with the fluoromethanes, one can estimate their rates by analogy to the methyl radical (CH3) reactions. We used rate expressions for these reactions, where the activation energy was reduced by 10% (relative to the corresponding methyl radical reaction) in order to compensate for the roughly 6 kJ/mol increase in the exothermicity of the reaction.
The experimental measurements (cited above) for abstraction of hydrogen by methyl and fluoromethyl radicals were all made at relatively low temperatures (about 300-600 K). Extrapolation of these measurements to flame decomposition temperatures may introduce significant uncertainty in the rates, especially since these reactions should have considerable non-simple Arrhenius temperature dependencies. In further refinements of this mechanism, these data should be critically evaluated. Experimental measurements at near flame temperatures would also be extremely valuable.
3.3.7. Fluoromethyl Radical Chemistry
Rate expressions for reactions involving the fluoromethyl radicals are labeled "NN" in Table 5.
Fluoromethyl radicals are destroyed by three general pathways whose relative importances are sensitive to conditions. 1) They can combine with H atoms forming chemically activated fluoromethanes that eliminate HF (creating methylene/fluoromethylenes). 2) They can react with oxygen-containing species (i.e., O2, O, OH), resulting in the formation of fluoromethoxy radicals and carbonyl fluoride species. 3) They can combine with methyl or fluoromethyl radicals, forming chemically activated fluoroethanes that may be either stabilized or eliminate HF (creating ethylene/fluoroethylenes). This latter class of reactions is included with the fluoroethane (C2) chemistry.
The fluoromethyl radicals are primarily formed by H atom abstractions from the fluoromethanes. However, there are several other channels that can contribute to their formation and are classified as C2 chemistry. For example, the reactions CH2=CHF + O => *CH2F + HCO and CHF2-CF2* + H => *CHF2 + *CHF2 contribute to the formation of fluoromethyl radicals. Similarly, there are a number of other decomposition channels that can be classified as C3 chemistry, such as *CH2F + C2H4 => *CH2-CH2-CH2F.
There are four potential reaction product channels following association of fluoromethyl radicals with O2 by analogy to hydrocarbon and chlorinated hydrocarbon chemistry. 1) Stabilization of the fluoromethylperoxy radicals (e.g., CHF2OO* product) or return to reactants (e.g., *CHF2 + O2). 2) Internal abstraction of a hydrogen atom followed by O-O bond breakage (e.g., CF2=O + OH products). 3) Internal abstraction of a fluorine atom followed by O-O bond breakage (e.g., CHF=O + OF products). 4) Direct dissociation of the O-O bond (e.g., CHF2O* + O products). The first channel (stabilization) should be negligible at flame temperatures (i.e., the adduct returns to reactants), but may need to be considered at lower temperatures and for ignition delays. The second channel (H abstraction) should be a secondary pathway at flame temperatures, but clearly should be reevaluated at lower temperatures. The third channel (F abstraction) can clearly be disregarded, because of the strong C-F bond. This contrasts to the analogous reactions that are assumed to occur in chlorinated hydrocarbon chemistry (e.g., Ho et al., 1992). Consequently, eliminating the first three potential product pathways, we must only explicitly consider the fourth channel (direct O-O bond dissociation) to form fluoromethoxy radicals and oxygen atoms (e.g., CHF2O* + O products).
There have been a number of rate measurements for the reaction of *CF3 with O2 near room temperature (Vedeneev et al., 1978; Ryan and Plumb, 1982; Caralp et al., 1986; Cooper et al., 1988; Orlando and Smith, 1988), but none (to our knowledge) for reaction of the other fluoromethyl radicals with O2. At low temperatures, the only possible product pathway is formation of the fluoromethylperoxy radical. These types of radical species are known to play a role in atmospheric chemistry. At high temperatures in a flame, these species will be present in significantly smaller concentrations and there are other possible product pathways for the fluoromethyl + O2 reactions. For *CF3 + O2 => CF3O* + O, we estimated a rate expression using RRKM analysis employing the reasonable assumption that there is no barrier in the reverse direction. For the reactions *CH2F + O2 => CH2FO* + O and *CHF2 + O2 => CHF2O* + O, we assumed the fluoromethoxy radical intermediate would be present in steady state concentrations and that it would rapidly eliminating HF after being formed. Based on these assumptions then, we simply used the *CF3 rate expression after adjusting for reaction enthalpies. For lower temperature conditions (than flames), these assumptions and the relevant reaction pathways and rate expressions should be reevaluated.
For reaction of the perfluoromethyl radical (*CF3) with O atoms (eliminating F), we used a rate constant corresponding to the room temperature value measured by McFadden and coworkers (Tsai et al., 1989). For reaction of the other fluoromethyl radicals with O atoms (eliminating H), we used rate constants scaled between that for *CH3 and *CF3. For reaction of the fluoromethyl radicals with OH radicals, we used rate constants identical to that for *CH3.
Fluoromethyl radicals are primarily destroyed in hydrocarbon flames through reactions with H, OH, and *CH3 radicals. Reactions with O atoms are minor channels. The biggest uncertainty here is likely the reactions with *CH3 radicals (HF elimination versus stabilization), which are very temperature and pressure dependent. Further refinements of this mechanism should provide better rate expressions for these reactions, benchmarking them to experimental data that exists (see brief discussion in Fluoroethane Chemistry section).
Reaction of fluoromethyl radicals with HO2 may be important for correctly describing ignition delays. There are two possible product channels: *CHF2 + HO2 => CH2F2 + O2 (disproportionation and chain termination) versus *CHF2 + HO2 => CHF2O* + OH (combination/elimination and chain propagation). We estimated rate expressions by analogy to the corresponding hydrocarbon reactions. We assumed that the fluoromethoxy radicals, once formed, immediately eliminate an H atom, since the C-H bond strengths are only 25-30 kJ/mol. This eliminates the need for explicitly including these species in the mechanism. For the CF3O* product, a fast subsequent F atom elimination step (which is explicitly included in the reaction mechanism) does not happen immediately, since the C-F bond dissociation energy is about 110 kJ/mol. If these reactions (for CH2FO* and CHF2O*) are shown to be important for ignition delays, then the rates and branching ratios should be reevaluated.
3.3.8. Fluoromethylene Destruction
Rate expressions for reactions involving the fluoromethylenes are labeled "NN" in Table 5.
Estimates for the rates of reactions of the fluoromethylenes (:CHF and :CF2) with many species are somewhat uncertain, because reactions involving these species are significantly slower than the analogous reactions for singlet methylene (1:CH2). Reactions of 1:CH2 are given in Table 5 (reactions HC29-34). There also appear to be conflicting experimental data on the reactivities of the fluoromethylenes. This will not be discussed here. The fluoromethylenes can be destroyed in a number of different ways.
1) The fluoromethylenes can be destroyed by reaction with H atoms, where we used rate expressions consistent with the room temperature values measured by McFadden and coworkers (Tsai and McFadden, 1989; Tsai and McFadden, 1990). These reactions are :CHF + H => *CH + HF and :CF2 + H => *CF + HF. For the reaction :CF2 + H (which is slightly slower), this necessitates employing a small activation barrier (5 kJ/mol) for the reaction.
2) The fluoromethylenes can be destroyed by reaction with O atoms, where we used rate expressions consistent with values measured at room temperature by Tsai and McFadden (1990). These reactions are :CHF + O => CO + HF and :CF2 + O => *CF=O + F. A small activation barrier (4 kJ/mol) for the :CF2 reaction was used.
3) The fluoromethylenes can be destroyed by reaction with OH radicals, where we used rate expressions consistent with a rate constant for reaction with CF2: (at 1090-1375 K) estimated by Biordi et al. (1978) in their flame measurements. Again a small barrier (14 kJ/mol) was used for :CF2 and no barrier for :CHF. There are at least two possible product channels for reaction of OH with each species: H atom elimination(s) and HF elimination. HF elimination is likely the secondary channel, because of both the barrier-to-elimination and a constrained transition state (lower A factor). We assigned an estimated branching ratio of kH/kHF=5 by analogy to other reactions.
4) The fluoromethylenes can be destroyed by reaction with HO2 radicals. The reaction of :CF2 with HO2 is major reaction pathway during ignition. We assigned rate constants referenced to the corresponding hydrocarbon reactions using kOH/kHO2=2 by analogy to reactions of OH and HO2 with CH3. There are two possible product channels: "abstraction" (e.g., CF2: + HO2 => *CHF2 + O2) versus combination/dissociation (e.g., CF2: + HO2 => CF2=O + OH). Again, we assigned an estimated branching ratio of kOH/kO2=5 by analogy to CH3 + HO2.
5) The fluoromethylenes can be destroyed by reaction with O2, where we used the rate expression for :CF2 measured by Keating and Matula (1977). This rate expression is also consistent with the measurements by Modica and LaGraff (1965) and Bauer et al. (1969). For :CHF, we used an equivalent rate expression (after adjusting for reaction enthalpy) with a significantly reduced, but still modest (24 kJ/mol) barrier. Since the :CHF reaction barrier has no experimental basis, if it is identified as a reaction that significantly contributes to the destruction of :CHF, then this reaction should be reevaluated. An ab initio transition state calculation would be extremely useful in resolving this uncertainty.
6) The fluoromethlyenes can be destroyed via insertion into H2O (a major flame species). We estimated barriers to reaction of 25 and 100 kJ/mol for :CHF and :CF2, respectively, from our BAC-MP4 ab initio transition state calculations.
7) The fluoromethylenes can also be destroyed via reaction with hydrocarbons (see brief discussion in Fluoroethane Chemistry section).
The fluoromethylenes (:CHF and :CF2) are largely destroyed in hydrocarbon flames via reaction with H atoms. Reactions with O and OH radicals are minor channels. There are good quality experimental data for all of the reactions, which proceed with small barriers. An open question here is the probable addition of the fluoromethylenes to ethylene. This class of reactions has been ignored in this mechanism in order to minimize the number of species in the reaction set, because these reactions would lead to the formation of C3 fluorinated hydrocarbons.
3.3.9. Fluoromethylidyne Radical Destruction
Rate expressions for reactions involving the fluoromethylidyne radical are labeled "NN" in Table 5.
The rates of reactions of fluoromethylidyne (*CF) with many species are somewhat uncertain given they are significantly slower than the analogous reactions for methylidyne (*CH). There also appear to be conflicting experimental data on its reactivity. This will not be discussed here. For the reactions of *CF with O2, H, and O, we used rate expressions with reasonable prefactors and barriers that are consistent with the room temperature rate measurements of McFadden and coworkers (Tsai et al., 1989; Tsai and McFadden, 1990) and Peeters et al. (1992). We note that to date we have (mis)assigned the products of the reaction *CF + H => C + HF (about 25 kJ/mol exothermic) as CH + F (about 20 kJ/mol endothermic). This was done to eliminate C, C2H, C4H2, and other fuel rich species in order to minimize the number of species in the reaction set. If a hydrocarbon sub-mechanism is used that includes these species, the correct product channel should be used. For *CF + OH => CO + HF, we assumed that there was no barrier to reaction. For *CF + H2O => Products, we estimated an activation energy of 70 kJ/mol by analogy to other Radical + H2O reactions.
*CF can also be formed via CH + HF => *CF + H2 (roughly 70 kJ/mol exothermic). We assumed that this reaction proceeds with no barrier, because of the high reactivity of CH. However, there may be a small barrier due to the strength of the HF bond. This reaction can be a major destruction pathway for CH in fluorine-inhibited hydrocarbon flames. Consequently, further refinements of this mechanism should provide a better estimate for this rate expression. A transition state structure and energy from ab initio calculations would be useful. An experimental measurement of this rate would be ideal. For reaction of *CF with other molecules, we assumed upper limits that should be reevaluated if those reactions are observed to contribute to *CF destruction.
In the reaction set, fluoromethylidyne (*CF) is largely destroyed via reaction with O2 and OH. Reaction with H atoms and H2O are minor channels. Given that there is no experimental measurements for reaction of *CF with H2O, limited (and inconsistent) data for reaction with O2, and both of these reactions are likely to have modest barriers, these reactions provide a significant uncertainty to this reaction set. Further refinements of this mechanism should address these issues for *CF, as well as for :CHF and :CF2.
3.3.10. Carbonyl Fluoride Chemistry
Rate expressions for reactions involving the carbonyl fluorides are labeled "PP" in Table 5.
An important set of species to fluorocarbon chemistry are the carbonyl fluorides (CHF=O, CF2O, *CF=O). CHF=O can be destroyed via unimolecular decomposition and H atom abstraction by H, O, and OH radicals. For the unimolecular decomposition (eliminating HF), we have fit the experimental data of Saito et al. (1985) using an extended Arrhenius expression (ATbe-E/RT) using the value for E0 (threshold energy) that they recommended based on their analysis. For the abstractions, we have substituted accepted rate expressions for the analogous CH2=O reactions. However, there is some significant uncertainty for abstraction by H atoms. The C-H bond dissociation energy in CHF=O is about 45-50 kJ/mol stronger than in CH2=O. Consequently, as an "abstraction" the barrier should be somewhat higher. On the other hand, H atom addition followed by H2 elimination could be more facile than the pure abstraction.
CF2=O can be destroyed via unimolecular decomposition (F atom elimination), by reactions with H atoms, through reactions with OH radicals, and through reactions, potentially, with H2O. The unimolecular decomposition is likely a negligible channel due to the strong C-F bond. There are a number of possible reactions with H atoms: 1) direct abstraction of a F atom abstraction; 2) addition to the oxygen followed by 1,2 elimination of HF; and 3) addition to the carbon followed by 1,1 elimination of HF. Biordi et al. (1974) have estimated a rate constant for the net reaction of H with CF2=O at 1800 K based on their molecular beam sampling measurements in low pressure flames. More recently, Richter et al. (1994) have estimated a rate expression based upon measurements at several different temperatures. We have also used BAC-MP4 ab initio transition state calculations (Zachariah et al., 1995) followed by RRKM analysis to provide rate expressions for each of the possible channels. Our calculations are in excellent agreement with the experimental values and indicate that the addition/1,2 elimination channel dominates (92 kJ/mol barrier), the addition/1,1 elimination channel is about a factor of ten slower (101 kJ/mol barrier), and the direct abstraction channel is negligible (188 kJ/mol barrier). Modeling results suggest that changes in flame speeds upon addition of fluorinated hydrocarbons are slightly sensitive to the rate of destruction of CF2=O.
CF2=O may also be destroyed via addition of OH to the carbon atom followed by 1,2-elimination of HF (Bozzelli et al., 1994). However, this is a likely minor channel for destruction, because we estimate a barrier of about 105 kJ/mol for the elimination step from our BAC-MP4 ab initio transition state calculations (Zachariah et al., 1995).
Because of the low reactivity of CF2=O and the large amounts of H2O in hydrocarbon flames, CF2O + H2O reactions must be considered. We have calculated (Zachariah et al., 1995) rate expressions for CF2=O + H2O complex formation followed by HF elimination. Flame modeling results suggest that reaction with water is a secondary destruction pathway to the H atom addition/1,2 elimination pathway. Nevertheless, it still needs to be considered.
*CF=O can be destroyed via unimolecular decomposition and reactions with H, O, OH, and *CH3 radicals. Flame modeling results suggest that the unimolecular decomposition and the reaction with H atoms are the primary decomposition pathways. For reaction with H atoms, we used a rate constant identical to that for the analogous HCO reaction. For the unimolecular decomposition, we determined a rate expression based on the reasonable assumption that combination reaction (reverse direction) is barrierless. There is significant uncertainty in the heat of formation of *CF=O and, consequently, there is significant uncertainty in this rate. Future refinements of this mechanism should address this issue. Flame modeling results suggest that the degree of inhibition is relatively sensitive to the rate of unimolecular decomposition of *CF=O.
3.4. C2 Fluorinated Hydrocarbon Chemistry
. . . Goto 3.5.
3.4.1. Overview
The C2 subset of the reaction set (approximately 450 reactions) consists of chemistry of 34 species containing two carbons (and hydrogen/fluorine/oxygen) with H, O, OH, H2O, and other flame species. The C2/H/F/O species used in this reaction set are the 9 fluoroethanes (e.g., CH2F-CF3), the 11 fluoroethyl radicals (e.g., CH2F-CF2*), the 5 fluoroethylenes (e.g., CHF=CF2), the 5 fluorovinyl radicals (e.g., CF2=CH*), the fluoroethynes (C2HF, C2F2), and the fluoroketenes and fluoroketyl radical (CHF=CO, CF2=CO, *CF=CO). As indicated earlier, only the (Z) forms of CHF=CHF, CHF=CH*, and CHF=CF* were considered to minimize the number of species in the reaction set.
The reaction set will not be described here in detail. Briefly, the fluoroethane destruction pathways (like fluoromethanes) consist of thermally and chemically activated decompositions and H atom abstraction reactions. Fluoroethyl radicals can react with H atoms creating fluoroethylenes via chemically activated fluoroethanes and HF elimination. Fluoroethyl radicals can also react with oxygen-containing species (O2, O, OH), resulting in the formation of oxidized fragments (e.g., CF3-CF2* + O => *CF3 + CF2=O). Fluoroethylenes (produced from thermally and chemically activated fluoroethane decompositions) are predominantly destroyed via reaction with O radicals, resulting in the formation of oxidized fragments (e.g., CH2=CF2 + O => *CH=O + *CHF2). Fluoroethylenes are also destroyed to a lesser degree through H atom abstraction by radicals such as OH, resulting in formation of fluorovinyl radicals (e.g., CH2=CF2 + OH => CF2=CH* + H2O). Fluorovinyl radicals (like fluoromethyl and fluoroethyl radicals) are destroyed via reactions with H radicals, as well as with oxygen-containing species.
3.4.2. Fluoroethanes: Thermally and Chemically Activated Decompositions
Rate expressions for thermally and chemically activated decompositions of the fluoroethanes are labeled "ED" in Table 5.
Both thermally and chemically activated decompositions of the fluoroethanes were considered, as well as stabilization of "hot" fluoroethanes (e.g., CH3-CF3 => CH2=CF2 + HF, *CH3 + *CF3 => CH2=CF2 + HF, and *CH3 + *CF3 => CH3-CF3). There have many measurements (mainly in shock tubes) of the unimolecular decomposition of the fluoroethanes. The kinetics of decomposition of most of the fluoroethanes (HF elimination) has been measured in a comprehensive series of work by Tschuikow-Roux and coworkers (Tschuikow-Roux et al., 1970; Tschuikow-Roux and Quiring, 1971; Tschuikow-Roux et al., 1971; Millward et al., 1971; Millward and Tschuikow-Roux, 1972; Sekhar and Tschuikow-Roux, 1974). Kinetic data for HF elimination from some of the fluoroethanes have also been obtained by Kerr and Timlin (1971) and Trotman-Dickenson and coworkers (Day and Trotman-Dickenson, 1969; Cadman et al.. 1970), Kochubei et al. (1980), and Mitin et al. (1988). We selected experimental values from these sources and used them without modification. The validity of employing these high pressure limit values should be reevaluated for those fluoroethanes which have only a few fluorine substitutions, especially when using the reaction set at low pressures (and high temperatures).
There have been a number of measurements for reactions involving chemically activated or "hot" fluoroethanes produced by combination of fluoromethyl radicals by Kim et al. (1973), by Trotman-Dickenson and coworkers (Kirk et al., 1968; Phillips and Trotman-Dickenson, 1968; Cadman et al., 1976), and by Pritchard and coworkers (Pritchard et al., 1964; Bryant and Pritchard, 1967; Bryant et al., 1967; Pritchard and Thommarson, 1967; Perona et al., 1968; Pritchard and Bryant, 1968; Pritchard and Perona, 1970; Follmer and Pritchard, 1974). Some of this work includes measurements of branching ratios between product channels (i.e., HF elimination versus stabilization). There are no measurements (to our knowledge) for decomposition of hot fluoroethanes following combination of fluoroethyl radicals and H atoms. We used rate expressions for all of the hot fluoroethanes for the various product channels from our RRKM analysis (Tsang, 1994) in order to provide a consistent set (see brief discussion in Section 3.5). Further refinements of this mechanism should include using all of the existing experimental data as reference values for the RRKM calculations.
3.4.3. Fluoroethanes: Fluoromethyl Disproportionations, Fluoromethylene Insertions
Rate expressions for fluoromethyl disproportionation and fluoromethylene insertion reactions are labeled "EC" in Table 5.
Pritchard and coworkers have made a comprehensive set of measurements of reactions involving disproportionations between (fluoro)methyl radicals (Pritchard and Follmer, 1973; Nilsson and Pritchard, 1982; Pritchard et al., 1984, 1985, 1987, 1990, 1991, 1992). These studies suggest a branching ratio for disproportionation versus combination (HF elimination or stabilization) of about 10-20% at 350-500 K. We employed these data in combination with estimated barriers from our BAC-MP4 ab initio transition state calculations and determined rate expressions consistent with the available experimental data. We estimated that the activation energies or barriers-to-disproportionation are about 3-9 kJ/mol for reactions involving *CHF2 (i.e., :CF2 product) and 14-19 kJ/mol for reactions involving *CH2F (i.e., :CHF product).
We also considered that :CHF and :CF2 may insert into C-H bonds in methane and the fluoromethanes. We used rate expressions based on estimated barriers for insertion from our BAC-MP4 ab initio calculations of 63 and 130 kJ/mol for :CHF and :CF2, respectively. These barriers are rather significant when compared to :CH2, which inserts into C-H bonds with little barrier. Our BAC-MP4 ab initio calculations suggest these barriers result from ionic repulsion between the electropositive H atom on the (fluoro)methane and the highly electropositive carbon atom on the fluoromethylene. For example, the H atom on CH4 has a Mulliken charge of +0.17 and the C atom on :CF2 has a Mulliken charge of +0.54. However, there is some experimental evidence to suggest that the barriers are significantly smaller (DiFelice and Ritter, 1994). This apparent conflict for these important species should be addressed in future mechanism refinements.
3.4.4. Fluoroethanes: Abstractions
Rate expressions for hydrogen abstractions from the fluoroethanes are labeled "EA" in Table 5.
There have been a number of measurements of hydrogen abstractions from fluoroethanes by OH radicals. Cohen and coworkers (Cohen and Benson, 1980; Cohen and Westberg, 1987) have used transition-state theory calculations to analyze and predict rate coefficients for a series of halogen-substituted methanes and ethanes. Much of their analysis is based on the experimental data of Clyne and Holt (1979) and Jeong et al. (1984). Other experimental data included in their analysis were from the measurements by Howard and Evenson (1976), Handwerk and Zellner (1978), Nip et al. (1979), and Martin and Paraskevopoulos (1983). In our work, we used the values recommended by Cohen and Benson (1987). For the three asymmetric fluoroethanes (CH3-CH2F, CH3-CHF2, CH2F-CHF2), where there are different functional H substitutions, we estimated the branching ratios based on relative bond strengths.
There have recently been a number of precise measurements for these abstraction reactions for a number of the fluoroethanes by Huie and coworkers (Liu et al., 1990; Zhang et al., 1992), by Ravishankara and coworkers (Talukdar et al., 1991; Gierczak et al., 1991), and by Nielsen (1991). Based on some of the more recent measurements there are newer recommendations by Cohen and Westberg (1991) for some of these reactions. The biggest changes are for reactions involving CH3-CHF2 and CHF2-CF3. However, the changes in the rate expressions are only significant at temperatures well below flame temperatures (because of Tb dependence).
Although there have been a number of measurements of hydrogen abstractions from many of the fluoroethanes by OH radicals, there have been no measurements (to our knowledge) for hydrogen abstractions by H and O atoms from any of the fluoroethanes. Consequently, in this work we utilized an empirical correlation that we determined for other hydrogen abstraction reactions. For hydrogen abstraction by H and O atoms, we used activation energies that were factors of 2.5 and 2.7 times, respectively, that for the analogous abstractions by OH radicals. These factors were based on the fact that the reactions with H and O atoms are about 62 kJ/mol and 70 kJ/mol less exothermic, respectively, than the corresponding reactions with OH.
The fluoroethanes are largely destroyed via unimolecular decomposition and abstraction by OH radicals. Good quality experimental data are available (cited above). Future refinements of this mechanism need only to reevaluate this work and, possibly, redetermine the branching ratios for the three asymmetric fluoroethanes. However, it would be valuable to have experimental measurements of these rates at flame temperatures, because hydrogen abstraction by OH are primary decomposition pathways and the recommended values are based on experimental measurements at relatively low temperatures (300-500K).
3.4.5. Fluoroethyl Radical Destruction
Rate expressions for reactions involving the fluoroethyl radicals are labeled "GG" in Table 5.
Fluoroethyl radicals can be destroyed via reaction with flame species such as O2, H, O, OH, and *CH3. For reactions with O2, O, and OH, we used rate expressions by analogy to those accepted for the corresponding ethyl radical reactions (Bozzelli and Dean, 1990; Baulch et al., 1992; Tsang and Hampson, 1986).
For reactions of O2 with the three fluoroethyl radicals without a beta hydrogen (CF3-CH2*, CF3-CHF*, CF3-CF2*), we assigned the products as *CF3 + CXY=O + O (i.e., C-C bond cleavage of CF3-CXY-O* intermediates). These products and rate expressions were chosen by analogy to the *CF3 + O2 reaction (adjusting for reaction enthalpy). Future refinements of this mechanism should consider formation of fluoroacetaldehyde species (and corresponding chemistry) following decomposition of the fluoroethoxy intermediates (e.g., CF3-CH2-O* => CF3-CHO (+H) => Products).
For reactions of O with the fluoroethyl radicals, two product channels must be considered. A third channel, abstraction of hydrogen, can be ignored by analogy to C2H5 + O. It is likely that H atom elimination (e.g., CH3-CHF* + O => CH3-CFO + H) is the dominant pathway over C-C bond cleavage (e.g., CH3-CHF* + O => CH3* + CHF=O). We assigned rate constants for the H atom elimination reactions relative to that for C2H5 using the geometric mean rule and scaling relative to the rate constants for CH3 + O and CF3 + O. In order to eliminate the fluoroacetaldehyde and (fluoro)acetylfluoride species from the reaction set (formed via the H atom elimination pathway), we assumed that these species are destroyed very quickly (that is, they are present only in steady state concentrations) and result in the eventual formation of (fluoro)ketene species. For example, a likely reaction pathway could be CH2F-CFO + H => *CHF-CFO + H2 followed by *CHF-CFO + H => [CH2F-CFO]* => CHF=CO + HF.
For reactions of OH with the fluoroethyl radicals, there are also two product channels that must be considered: combination/HF elimination (e.g., CH3-CHF + OH => CH3-CHO + HF) versus hydrogen abstraction (e.g., CH3-CHF + OH => CH2=CHF + H2O). We have ignored several other possible channels. HF elimination involving breaking a C-H bond (e.g., CH3-CHF + OH => CH2=CH(OH) + HF) will have a higher barrier than breaking a O-H bond (e.g., CH3-CHF + OH => CH3-CHO + HF). Product channels involving breaking a C-C bond (e.g., CH3-CHF + OH => *CH3 + *OCH2F) were also ignored. In contrast to that for O atoms, abstraction of beta hydrogen atoms from ethyl radicals by OH radicals is generally assumed to occur. We assigned rate constants for the two possible channels employing the corresponding rate constants for the analogous reactions with O atoms. A small barrier (about 12 kJ/mol) was estimated for the abstraction channel. As for the fluoroethyl + O reactions, we assumed that the fluoroacetaldehyde and (fluoro)acetylfluoride species are quickly destroyed, resulting in the formation of (fluoro)ketene species.
Fluoroethyl radicals may also react with H atoms and form "hot" fluoroethanes. For these reactions we used rate expressions from our RRKM calculations (as mentioned previously). Fluoroethyl radicals may combine with *CH3 to form hot fluoropropanes (which are likely to be stabilized except at the highest temperature). Fluoroethyl radicals may also disproportionate with *CH3 to form CH4 and fluoroethylenes. The first channel (combination) was simply ignored in order to exclude C3 fluorinated species from the reaction set. The rate constants for the second channel (disproportionation) were set identical to that accepted for the reaction *C2H5 + *CH3 => C2H4 + CH4 (Tsang and Hampson, 1986).
3.4.6. Fluoroethylenes: Decompositions and Reactions with H
Rate expressions for thermally and chemically activated decompositions of the fluoroethylenes are labeled "JD" in Table 5. Rate expressions for reactions of H atoms with the fluoroethylenes are labeled "JA" in Table 5.
In this work, we used experimental rate expressions (Simmie and Tschuikow-Roux, 1970; Simmie et al., 1970) for the rate of pyrolysis (eliminating HF) of two of the fluoroethylenes (CH2=CHF and CH2=CF2). For the other fluoroethylenes, we used these rate expressions as reference points and adjusted the activation energy based on the reaction enthalpy. For thermal decomposition or pyrolysis of perfluoroethylene (CF2=CF2 => :CF2 + :CF2), we used rate expressions from our RRKM analysis of the experimental data of Schug and Wagner (1978). These data are also consistent with experimental rate expression of Modica and LaGraff (1966). For the other thermally and chemically activated fluoroethylene decomposition channels (e.g., :CHF + :CHF => CHF=CHF or C2HF + HF), we used rate expressions from our RRKM calculations (based on the reverse reactions or combinations).
Fluoroethylenes can also be destroyed via reaction with H atoms. This includes H atom addition followed by stabilization of the fluoroethyl radical produced (e.g., CH2=CF2 + H => CH3-CF2* or CHF2-CH2*), as well as H atom addition followed by F atom elimination (e.g., CH2=CF2 + H => CH2=CHF + F). There are some experimental data for these reactions (e.g., Teng and Jones, 1972, 1973), however, there appears to be some conflict between them. Consequently, in this mechanism, we simply employed an accepted rate expression for the H atom addition/stabilization for the analogous ethylene reaction. That is, we used rate expressions for the reactions of fluoroethylenes with H atoms by analogy to the recommendations of Tsang and Hampson (1986) for the two pathways C2H4 + H => C2H5 and C2H4 + H => C2H3 + H2. For the other possible pathway for reaction of H atoms with the fluoroethylenes (H atom addition and F atom elimination or displacement), we assumed barrierless addition of fluorine atoms.
There are some significant uncertainties here for the H atom addition reactions. First, it is likely the barrier-to-addition will be influenced by the degree of fluorine substitution on the alpha carbon. Secondly, the efficiency of stabilization of the chemically activated or "hot" fluoroethyl radical will be strongly influenced by the degree of fluorine substitution. Further refinements of this mechanism should address these issues. For example, reasonable estimates for the relative barriers-to-addition could be obtained from BAC-MP4 ab initio transition state calculations and the relative stabilization efficiencies could be estimated reasonably well using RRKM analysis.
The fluoroethylenes should also react relatively quickly with methyl and fluoromethyl radicals and with methylene and the fluoromethylenes. However, we have not included these reactions in the reaction set, because they lead to the formation of C3 fluorinated hydrocarbons (essentially polymerization reactions). Future refinements of this mechanisms should investigate the potential influence of these type of reactions on the overall chemistry.
3.4.7. Fluoroethylenes: Reactions with O and OH
Rate expressions for reactions of O and OH with the fluoroethylenes are labeled "JO" in Table 5.
The fluoroethylenes are primarily destroyed via reaction with O atoms (e.g., CH2=CF2 + O => *CHF2 + HCO). For these reactions, we used rate expressions that were fits to extended Arrhenius form (ATbe-E/RT) to the recommendations of Cvetanovic (1987) in order to extrapolate the low temperature measurements (300-500 K) to flame temperatures. A temperature dependence of T1.0 was used by analogy to other reactions involving O atoms. The recommended values by Cvetanovic are largely based on work in this area by Herron and Huie (1973), Jones and Moss (1974), Atkinson and Pitts (1977), and Gutman and coworkers (Park et al., 1984). It should be noted that for perfluoroethylene, the only possible channel is CF2=CF2 + O => CF2=O + :CF2 (i.e., no H migration possible). It should also be noted that for CH2=CHF there are two possible channels ("addition" of the O atom to one side or the other). We have used an estimated additional 4 kJ/mol for "addition" of the O atom to the fluorinated carbon. This is consistent with an upper limit measurement at room temperature for this reaction by Gutman and coworkers (Slagle et al., 1974).
For reaction of O with the fluoroethylenes, it is generally understood that the dominant pathway is where the products are the fluoromethyl and (fluoro)formyl radical (e.g. CH2=CHF + O => HCO + *CH2F) following dissociation of the chemically activated fluoroethylene oxide formed by O atom attack on the double bond. That is, the O atom first "adds" to the carbon with the least number of electronegative substituents (in this case F). An H atom on this carbon, then "migrates" to the other carbon. However, there is some evidence (Gilbert et al., 1976) to suggest that the assumed methyl+formyl products (e.g., *CHF2 + HCO) may not be the only product channel (e.g., CHF=CHF + O => CHF=C=O + HF or CHF=CHF + O => CHF=O + :CHF). The numerous other possible channels are generally considered to be minor pathways: 1) stabilized fluoroethylene oxides, 2) stabilized fluoroacetaldehydes, 3) fluoroacetyl radicals + H, 4) fluorovinoxy radicals (e.g., *CHF-CFO) + H, 5) (fluoro)formaldehydes + (fluoro)methylenes, 6) fluoroketenes + H2, and 7) fluorovinyl radicals + OH. The latter class of reactions, hydrogen abstraction, is a separate reaction from the first four (which are additions) and may become important at the highest temperatures. Given that the reaction of O with the fluoroethylenes is a primary decomposition pathway for the fluoroethylenes and that the rate expressions are based on experimental measurements at low temperatures (300-500 K), it would be very valuable to have measurements of these reactions and product channels at near flame temperatures. ab initio transition state calculations could shed some light on the relative importance of each potential reaction pathway.
Fluoroethylenes can also be destroyed via reaction with OH radicals. We have only considered H atom abstraction (and not addition/elimination). For abstraction of H atoms from the fluoroethylenes by OH radicals, we used rate expressions that were fits (with an estimated T2.0 dependence) to the values recommended by Baulch et al. (1992) for C2H4 + OH => C2H3 + H2O, which is based on a measurement by Tully (1988). Clearly the C-H bond strength will be significantly influenced by fluorine substitution. This issue should be addressed in future refinements of this mechanisms.
Fluoroethylenes may also be destroyed by OH addition/elimination reactions. This could result in the formation of fluoroethenols (e.g., CHF=CH(OH) ) or possibly fluorovinoxy radicals (e.g., *CHF-CFO). There are a number of uncertainties here and, consequently, these reaction pathway were not pursued. First, these pathways result in the production of a number of new species in the reaction set, whose thermochemistry is unknown. Second, decomposition pathways for these new species must be considered. Third, the effect of fluorine substitution on the barrier to OH addition is not known (but probably could be estimated reasonably well using RRKM analysis). Fourth, the relative rates for at least three competing reactions must be known; that is, 1) stabilization of the fluorohydroxyethyl radicals (e.g., *CF2-CF2-OH) versus reversion to reactants, 2) H atom elimination, and 3) HF elimination. Future refinements of this mechanism should investigate the potential importance of the OH addition/elimination reactions for the fluoroethylenes. It may be that only the perfluorocompounds may need to be considered (by analogy to the sole importance of the perfluoromethoxy radical).
3.4.8. Fluorovinyl Radical Destruction
Rate expressions for reactions involving the fluorovinyl radicals are labeled "JO" in Table 5.
Westmoreland (1992) has calculated the temperature (and pressure) dependencies of the rate for the chemically activated reaction C2H3 + O2 => CH2O + HCO. We used these values for the analogous fluorovinyl radical reactions. In this work, we used the values recommended by Warnatz (1984) and Tsang and Hampson (1986) for the C2H3 + O => Products and C2H3 + OH => Products reactions, respectively, for the analogous fluorovinyl radical reactions. The values recommended by Warnatz for the first reaction is based on measurements by Heinemann et al. (1988).
3.4.9. Fluoroethyne, Fluoroketene, and Fluoroketyl Radical Chemistry
Rate expressions for reactions involving these species are labeled "KK" in Table 5.
For reactions involving the fluoroethynes (C2HF, C2F2), the fluoroketenes (CHF=C=O, CF2=C=O), and the fluoroketyl radical (*CF=C=O), we used rate expressions by analogy to the corresponding hydrocarbons (C2H2, CH2CO, *HCCO). For reaction of H atoms with the two fluoroethynes (C2HF, C2F2), we used rate expressions derived from the recommendation of Warnatz (1984) for C2H2 + H => C2H3, which is based on measurements by Payne and Stief (1976). For these H atom addition reactions, we employed third-body stabilization efficiencies and low pressure limits identical to that for acetylene. Future refinements of this mechanism should provide better estimates for these reactions.
3.5. RRKM Analysis
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Rate constants for chemical activation process were determined through solution of the steady state master equation in the context of a step ladder model and transition states that satisfy the high pressure rate expressions. Extension to multichannel decomposition is straightforward in the sense of simply adding another term to the expressions involving the decomposition channels. The step-size down parameters are taken to be T/3 cm-1 and lead to values near 500 cm-1 under conditions relevant to combustion. These numbers are consistent with fall-off data. The general procedure for RRKM analysis (Robinson and Holbrook, 1972) is in contrast to the treatment of weak collisions generally described as the QRRK procedure (Dean and Westmoreland, 1987). This procedure is of some validity for describing single channel unimolecular decompositions, since Troe (1977) has derived a relationship between the collision efficiency and the step-sizes down. However, for chemically activated processes, which are really the simplest type of multichannel decompositions, this collisional efficiency is no longer related to the step-sizes. As such, it is thus an arbitrary fit parameter. Without experimental data, it is not clear how to assign this parameter. The situation is even worse when there is multiple decomposition channels. Strictly speaking, one would need to define a collision efficiency for every channel. Here again, there is at present no basis for assigning these values.
The assignment of the high pressure rate expression is a key element in each estimation. Our procedure is to utilize experimental data were it exists. In the absence of reliable experimental data, the high pressure rate expression is derived by analogy; for example, using the geometric mean rule. For combination reactions involving radicals, this approach is consistent with Benson's geometric approach (Benson, 1976) leading to the restricted rotor transition states that are used in this work. Thus, the combination rate expressions (Tsang, 1994) for the (fluoro)methyl radicals are based on k(CH3 + CH3 => C2H6) and k(CF3 + CF3 => C2F6). For the reactions of hydrogen atoms with (fluoro)methyl radicals, the combination rate expressions are based on k(CH3 + H => CH4) and k(CF3 + H => CHF3).
3.6. BAC-MP4 Ab Initio Predictions
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For a number of reactions considered in the mechanism, there are no or little experimental rate data. Consequently, we have estimated that data using BAC-MP4 ab initio calculations of the transition state geometries and energies and RRKM/master equation analysis. A short description of the BAC-MP4 ab initio calculations is given in the section titled Thermochemistry: BAC-MP4 ab initio Predictions. The transition state for a reaction was obtained by searching for a geometry with one negative eigenvalue. This corresponds to a saddle point on the potential energy surface. This is then followed by a steepest-descent reaction path analysis to ensure that the calculated transition state corresponds to the appropriate reactants and products. BAC corrections are then assigned in the same manner as with the equilibrium structures. In order to quantify the uncertainties in the calculated data, we have also performed calculations on a number of related reactions where there is good quality experimental data.
We have calculated transition states for a number of sets of reactions, including the following:
1. HF elimination from the fluoromethanes (e.g., CH3F => :CH2 + HF);
2. H2 elimination from the fluoromethanes (e.g., CH3F => :CHF + H2);
3. H atom abstraction by H from the fluoromethanes (e.g., CH3F + H => *CH2F + H2);
4. F atom abstraction by H from the fluoromethanes (e.g., CH3F + H => *CH3 + HF);
5. reactions of H2O with the fluoromethylenes (e.g., :CHF + H2O => CH2FOH => CH2O + HF);
6. reactions of H2O with carbonyl difluoride (e.g., CF2=O + H2O => FCO2H + HF);
7. F atom abstraction by H from carbonyl difluoride (i.e., CF2=O + H => *CF=O + HF);
8. H atom addition to carbonyl difluoride (e.g., CF2=O + H => *CF2OH => *CF=O + HF);
9. OH addition to carbonyl difluoride (i.e., CF2=O + OH => *OCF2(OH) => FC(O)O* + HF).
The ab initio geometries and energies of the transition states were then used as inputs to RRKM/master equation analysis in order to calculate rate expressions. The calculated rate expressions agree well with those derived from experimental measurements (where they exist). Further discussion of the ab initio transition state calculations can be found elsewhere (Zachariah et al., 1995).
There is one reaction that is very important to the chemistry of fluorinated hydrocarbon destruction and where the calculated rate expression can be compared with good quality experimental measurements. The rate of reaction of H atoms with CF2=O has been estimated based on measurements in flames of the rate of disappearance of carbonyl difluoride. Biordi et al. (1974) estimated a rate constant at 1800 K for this reaction in CF3Br inhibited methane/oxygen/argon premixed flames. More recently, Richter et al. (1994) have determined rate coefficients at 1175-1490 K for this reaction in CF3H inhibited hydrogen/oxygen/argon premixed flames.
The reaction of H atoms with CF2=O has three distinct pathways, one is a direct abstraction and the other two are addition/elimination reactions.
First, H atoms can abstract fluorine (i.e., CF2=O + H => *CF=O + HF). Our BAC-MP4 transition state calculations suggest a barrier of about 150 kJ/mol for this reaction. This compares well with calculated barriers of about 130-170 kJ/mol for F atom abstraction from the fluoromethanes. These calculated barriers are consistent with that measured by Kochubei and Moin (1971) for F atom abstraction by H from CF4. They reported an activation energy of about 190 kJ/mol at 1200 K-1600 K. This would suggest a barrier of about 160 kJ/mol assuming a T2.0 dependence to the rate.
The second pathway consists of H atom addition to the carbon atom on the carbonyl difluoride followed by 1,1 elimination of HF from the chemically activated fluoromethoxy intermediate (i.e., CF2=O + H => [CHF2O*]* => *CF=O + HF). The third pathway is also an addition/elimination reaction, but consists of H atom addition in this case to the oxygen atom on the carbonyl difluoride followed by 1,2 elimination of HF from the "hot" hydroxyfluoromethyl intermediate (CF2=O + H => [*CF2OH]* => *CF=O + HF).
Our ab initio transition state calculations suggest barriers of about 50 kJ/mol and 65 kJ/mol for addition to the carbon and oxygen sides of the carbonyl difluoride, respectively. It is slightly more energetically favorable for the H atom to add to the carbon side. However, the subsequent 1,1 HF elimination step in this case in order to form the *CF=O product involves a transition state that is an additional 80 kJ/mol higher (a total of 130 kJ/mol). The overall energetics of this pathway is significantly less favorable than the 1,2 HF elimination step that follows H atom addition to the oxygen side. This involves a transition state that is only additional 15 kJ/mol higher (a total of 80 kJ/mol). We have derived rate expressions based on RRKM/master equation calculations using the geometries and energies of the ab initio transition states. These calculated rate expressions (Zachariah et al., 1995) agree extremely well with the experimental rate constants reported by Biordi et al. (1974) and Richter et al. (1994).
Further discussion of the ab initio transition state calculations can be found elsewhere (Zachariah et al., 1995).
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