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.
2. Thermochemistry
2.1. Overview
. . . Goto 2.2.
Existing thermochemical data were compiled and evaluated. Where little or no data existed for potential species of interest (most of the radicals), we estimated that thermochemistry using both empirical methods, such as group additivity (Benson, 1976), and also through application of ab initio molecular orbital calculations (Melius, 1990; Curtiss et al., 1991; Frisch et al., 1992). In all cases (experimental, empirical, and ab initio), significant effort was made to utilize thermochemical data for each species that was consistent with data for all other species.
There are a number of general sources of relevant compiled and evaluated thermochemical data. These include The Chemical Thermodynamics of Organic Compounds (Stull et al., 1969), JANAF Thermochemical Tables (Stull and Prophet, 1971; Chase et al., 1985), Thermochemical Data of Organic Compounds (Pedley et al., 1986), TRC Thermodynamic Tables (Rodgers, 1989), Physical and Thermodynamic Properties of Pure Chemicals (Daubert and Danner, 1985), NIST Structures and Properties Database and Estimation Program (Stein et al., 1991), and Thermodynamic Properties of Individual Substances (Gurvich et al., 1991).
There are two compilations/evaluations of fluorinated hydrocarbons in the Journal of Physical and Chemical Reference Data: "Ideal Gas Thermodynamic Properties of Six Fluoroethanes" (Chen et al., 1975) and "Ideal Gas Thermodynamic Properties of Halomethanes" (Kudchadker and Kudchadker, 1978). There are two compilations/evaluations of fluorinated hydrocarbons in the Russian Chemical Reviews: "Thermochemistry of Halogenomethanes" (Kolesov, 1978) and "Thermochemistry of Haloethanes" (Kolesov and Papina, 1983).
There are a several individual sources of more recent data for thermochemistry that are relevant. These include "Thermochemistry of Fluorocarbon Radicals" (Rodgers, 1978), "Hydrocarbon Bond Dissociation Energies" (McMillen and Golden, 1982), "A Kinetic Study of the Reactions of OH Radicals with Fluoroethanes. Estimates of C-H Bond Strengths in Fluoroalkanes" (Martin and Paraskevopoulos, 1983), and "Halomethylenes: Effects of Halogen Substitution on Absolute Heats of Formation" (Lias et al., 1985).
There are numerous other references with thermodynamic data for fluorinated hydrocarbons that we have compiled as part of this work. These are included in the Bibliography section and some of them will be cited and, possibly, be discussed in more detail in the relevant sections. References for thermochemical data can be found in the Bibliography: Section 6.2. General Thermochemistry and Kinetics; Section 6.3. Hydrocarbon Chemistry; Section 6.4. Fluorine Chemistry; Section 6.5. Fluorocarbon Thermochemistry; and Section 6.6. Oxidized Fluorocarbon Thermochemistry.
It should be noted that for some of the stable species and for many of the radicals, we have relied upon recent ab initio calculations of thermochemical data. This includes both ab initio calculations done as part of work and those done previously by other workers. Tschuikow-Roux and coworkers have calculated thermochemistry for the fluoroethyl radicals (Chen et al., 1990; Chen et al., 1991). Nyden et al. (1994) have used ab initio calculations to obtain thermochemical data for a number of the fluoroethanes and fluoroethyl radicals. A brief discussion of the BAC-MP4 calculations can be found in Section 2.5. Further details of these calculations can be found elsewhere (Burgess et al., 1994; Zachariah et al., 1995). More recent thermochemistry for other ab initio calculations may be found elsewhere (Berry et al., 1995).
The thermochemical data that was used is given Tables 1-3 for hydrogen/oxygen and hydrocarbon species (Table 1), H/F species and C1 fluorocarbons (Table 2), and C2 fluorocarbons (Table 3). These tables include enthalpies of formation, entropies at standard state, and temperature-dependent heat capacities. Comparisons between our calculated values (Zachariah et al., 1995) and different literature values (experimental, estimated) for heats of formation are given in Table 4. Reported uncertainties in the literature values are also given in Table 4.
A discussion of the uncertainties in the thermochemical data is given in the text with each class of species. The literature values include those that have been calculated using ab initio methods. A critical evaluation of the ab initio values in comparison with experimentally derived values is given elsewhere (Zachariah et al., 1995). In each case where the uncertainty in the data from the literature was not assigned, we have provided a value based on our evaluation of the data and typical uncertainties for that type of data.
The literature values for heats of formation consist of a number of different types of data. Many are good quality, experimentally derived values based on heat of combustion or heat of reaction data, where the other reactants and products have well-established heats of formation. The uncertainty in these data are typically less than 4 kJ/mol. Some of the data, although experimentally derived, have somewhat higher uncertainties due to side reactions or where the other reactants and products have somewhat uncertain heats of formation. Typically, these values have heats of formation with uncertainties of about 4-8 kJ/mol.
In some cases, the literature values are based, in whole or in part, on bond additivity, group additivity, or other trends in heats of formation of related species. Typically, these values have heats of formation with uncertainties of about 8-12 kJ/mol. Many of the radicals have literature values for their heats of formation that were determined using the heats of formation of the parent species and bond dissociation energies that were either indirectly measured or were reasonable estimates based on trends in other molecules. For example, Martin and Paraskevopoulos (1983) have estimated C-H bond strengths in fluoromethanes and fluoroethanes (and, consequently, heats of formations for the fluoromethyl and fluoroethyl radicals) through correlations between the rates of H atom abstraction by OH radicals, C-H vibrational frequencies, and known C-H bond strengths. We have supplemented these data with our own estimates in order to provide heats of formation for the other fluoroethyl radicals in the absence of other literature values.
The thermochemical data in Tables 1-3 include entropy and temperature dependent heat capacity data, in addition to heat of formation data. References for all of these data are given in those tables. In the following sections, there is no comparisons or discussion of the entropy and heat capacity data, because in most cases there is only a single source of data. Furthermore, the uncertainties in these data are largely dependent upon uncertainties in low frequency bonds and barriers-to-rotation (for molecules with hindered rotors) and it is outside the scope of this work to quantitatively evaluate these data. The reader is referred to the original sources. However, based on inspection of the experimentally derived entropies, as well as comparing these data to that calculated using ab initio structures, one concludes that uncertainties in entropies at standard state are typically less than 0.5 J/mol/K. Where there is uncertainty in low frequency modes or barriers to rotation, uncertainties in entropies increase to about 2 J/mol. These values correspond to uncertainties in equilibrium constants of about 5-30% (and thus, any rate constants calculated using equilibrium constants). In contrast, uncertainties in heats of formation are typically on the order of 8 kJ/mol. This corresponds to a significantly higher uncertainty in the rate constants; for example, a factor of 2 at 1500K. That is, uncertainties in rate constants due to uncertainties in entropies at standard state are typically very small compared to that due to uncertainties in heats of formation.
2.2. H/O/F and Hydrocarbon Species
. . . Goto 2.3.
We used standard hydrogen/oxygen and hydrocarbon thermochemistry (see Table 1), most of which can be found in the JANAF tables (Stull and Prophet, 1971; Chase et al., 1985) or in a Sandia compilation (Kee et al., 1987), as can data for F and HF (see Table 2). There is a more recent value for the heat of formation of HF (Johnson et al., 1973). However, we used the JANAF value for consistency, because many thermochemical and rate data for fluorinated species are based on the JANAF recommendation. More recent data on thermochemistry for C2H3 and HCO have been utilized. Future mechanism refinements should include re-adjustment of any other thermochemistry (or rate constants) that are based upon older values for the heat of formation of these species.
Other simple species (e.g., F2, FO*, HOF, FOF, FOO*, HOOF) were initially considered in the mechanism but were later excluded because they did not contribute to the overall chemistry. For this reason, thermochemical data for these species are not included in Table 2.
2.3. C1 Fluorinated Hydrocarbons
. . . Goto 2.4.
2.3.1. Fluoromethanes
We chose to employ heats of formation for the fluoromethanes as recommended by Kolesov (1978) with the entropy and heat capacity data found in a review article (Rodgers et al., 1974) in the Journal of Physical and Chemical Reference Data (JPCRD). We have calculated heats of formation for the fluoromethanes (Zachariah et al., 1995) using the BAC-MP4 method (Melius, 1990) and find the calculated values to be within about 2 kJ/mol of these recommended literature values (see Table 4).
There are a number of sources of compiled or evaluated thermochemical data for the fluoromethanes (CH3F, CH2F2, CHF3, and CF4). Thermochemical data for the fluoromethanes has been reviewed by Lacher and Skinner (1968), by Stull et al. (1969), and by Cox and Pilcher (1970). Thermochemical data can also be found in the JANAF tables (Stull and Prophet, 1971), has been reevaluated subsequently in JPCRD (Rodgers et al., 1974), by Pedley et al. (1986), and by Gurvich et al. (1991). The most recent edition of the JANAF tables (Chase et al., 1985) did not reevaluate thermochemical data for the fluoromethanes. Recommendations for the heats of formation of the fluoromethanes have been also been made by Kolesov (1968). Gelles and Pitzer (1953) have tabulated entropies at standard state and heat capacities as a function of temperature for the fluoromethanes (and other halogenated methanes).
Heats of formation for CH2F2 and CF4 are the best known, with uncertainties of less than 1.5 kJ/mol, and are derived from their heats of combustion. The recommended value for the heat of formation of CH2F2 is based on a measurement by Neugebauer and Margrave (1958) of the heat of combustion of CH2F2. The heat of formation of CF4 is based on measurements of a number of different heats of reactions involving CF4 by Scott et al. (1955), Good et al. (1956), Neugebauer and Margrave (1956), Cox et al. (1965), Wood et al. (1967), Domalski and Armstrong (1967), and Greenberg and Hubbard (1968).
The heat of formation of CHF3 has a slightly higher uncertainty (than for CH2F2 and CF4) of about 4 kJ/mol due to side reactions (producing CF4) in its combustion. The recommended value for the heat of formation of CHF3 is based on a heat of combustion measurement by Neugebauer and Margrave (1958). The heat of formation of CHF3 has also been calculated using equilibrium data with CF3Br and CF3I as measured by Corbett et al. (1963), Goy et al. (1967), Coomber and Whittle (1967). The heat of formation of CHF3 can also be calculated assuming a heat of formation for *CF3 and kinetic data (forward and reverse reactions) involving HCl, HBr, and HI as measured by Coomber and Whittle (1966), Amphlett and Whittle (1968), and Goy et al. (1967), respectively.
The heat of formation of CH3F has been estimated (with an uncertainty of about 10 kJ/mol) employing empirical trends in heats of formation of the other fluoromethanes, since there are no experimentally derived values (other than from appearance potential measurements). Although CH3F is unlikely to be a key species in fluorinated hydrocarbon-inhibited hydrocarbon flames, as the simplest fluorinated hydrocarbon, its heat of formation is significant as a reference point for heats of formation of other fluorinated hydrocarbons. Empirical estimates for the heat of formation of CH3F have also been made by Zahn (1934), Allen (1959), Bernstein (1965), Rodgers (1967), and Lacher and Skinner (1968). The recommended value in the JANAF tables (Stull and Prophet, 1971) is based on appearance potentials for CH3+ from CH3F measured by Lossing et al. (1954). Dibeler and Reese (1955) and Tsuda et al. (1964) have also measured roughly the same appearance potential.
2.3.2. Fluoromethyl Radicals
We chose to employ heats of formation for the fluoromethyl radicals as recommended by McMillen and Golden (1982). For entropies at standard state and heat capacity data, we used values for *CF3 from the JANAF tables. Since (to our knowledge) no experimentally derived entropy and heat capacity data exist for *CH2F and *CHF2, we used that derived from our BAC-MP4 ab initio calculations. Heats of formation for the fluoromethyl radicals estimated using the BAC-MP4 method are within about 4 kJ/mol of these recommended literature values (see Table 4).
There are several sources of compiled or evaluated thermochemical data for the fluoromethyl radicals. Thermochemical data for the perfluoromethyl radical (*CF3) can be found in the JANAF tables (Stull and Prophet, 1971) and have been reevaluated subsequently by Rodgers (1978). The heat of formation of *CF3 has an uncertainty of about 5 kJ/mol. Experimentally derived heats of formation (from bond dissociation energies and heat of reactions) for all of the fluoromethyl radicals (*CH2F, *CHF2, *CF3) can be found in evaluations by McMillen and Golden (1982) and Pickard and Rodgers (1983) with uncertainties of less than 10 kJ/mol.
The evaluated thermochemical data for *CH2F and *CHF2 are based on a number of different experimental measurements. Okafo and Whittle (1974) have used heat of reaction data to determine the bond dissociation energy for CHF2-Br, from which the heat of formation of *CHF2 can be calculated. Martin and Paraskevopoulos (1983) have measured the rates of reaction of OH with some fluoromethanes and fluoroethanes and developed correlations between C-H bond dissociation energies, C-H stretching frequencies, and rates of abstraction of H atoms by OH radicals from fluoroalkanes. From heats of formation of the parent fluoromethanes and estimated C-H bond dissociation energies, one can determine values for the heats of formation of *CH2F, *CHF2, and *CF3. Whittle and coworkers have used heat of reaction data to determine the bond dissociation energies of CHF2-H and CHF2-Br (Okafo and Whittle, 1974), from which the heat of formation of *CHF2 can be calculated. Using kinetic data, bond dissociation energies for CH2F-H have obtained by Pritchard and Perona (1969) and for CHF2-H by Kerr and Timlin (1971), from which one can calculate the heats of formation of the corresponding radicals.
The evaluated thermochemical data for *CF3 are based on a number of different experimental measurements. The heat of formation of *CF3 has been calculated assuming a heat of formation for CHF3 and kinetic data (forward and reverse reactions) involving HCl, HBr, and HI, as measured by Coomber and Whittle (1966), Amphlett and Whittle (1968), and Goy et al. (196 7), respectively. It can also be calculated assuming a heat of formation of CF3I and kinetic data for its reaction with I2, as determined by Coomber and Whittle (1966). Pritchard and Thommarson (1964) used kinetic data from competing reactions to determine the CF3-H bond dissociation energy and, consequently, the heat of formation of *CF3 can be calculated assuming a heat of formation for CHF3. Whittle and coworkers have used heat of reaction data to determine the bond dissociation energies for CF3-CF3 (Coomber and Whittle, 1967), CF3-Br (Ferguson and Whittle, 1972), and CF3-I (Okafo and Whittle, 1975), from which the heat of formation of *CF3 can be calculated. Tsang (1986) has determined a value for the heat of formation of *CF3 based on the bond dissociation energy of CF3-Br from shock tube decomposition studies. Skorobogatov and coworkers have measured equilibrium constants for reactions of type CF3-X <=> *CF3 + X and CF3-X + X <=> *CF3 + X2 and determined bond dissociation energies for CF3-Br (Dymov et al., 1991) and CF3-I (Skorobogatov et al., 1991).
2.3.3. Fluoromethylenes and Fluoromethylidyne Radical
We used heats of formation for :CF2 as adopted by Rodgers (1978) and for :CHF as provided by Pritchard et al. (1984). For entropies at standard state and heat capacity data of both species, we used values from the JANAF tables. We have calculated heats of formation for the fluoromethylenes (Zachariah et al., 1995) using the BAC-MP4 method and find the calculated values to be within about 15 kJ/mol of these recommended literature values (see Table 4).
There are several sources of thermochemical data for the closed-shell fluoromethylenes (:CHF and :CF2). Thermochemical data for these species can be found in the JANAF tables (Stull and Prophet, 1971). Rodgers (1978) has recommended a value for the heat of formation of :CF2 based largely upon kinetic data. Hsu et al. (1978) and Pritchard et al. (1984) have independently made a recommendation for the heat of formation of :CHF based upon heat of reaction and kinetic data. Lias et al. (1985) have provided values for the heat of formation of both :CHF and :CF2 based upon appearance and ionization potentials. Unfortunately (since :CHF and :CF2 are important species), there are significant uncertainties in their heats of formation. The values for :CF2 are the best (+/- 10 kJ/mol) and are derived from a number of different types of measurements. The uncertainty in the heat of formation for :CHF is even greater (+/- 30 kJ/mol) due to the lack of direct, reliable data.
The experimental data for the heat of formation of :CF2 comes from a number of different measurements. The heat of formation of :CF2 has been calculated from heat of reaction or kinetic data from the decomposition of C2F4 by Modica and LaGraff (1965, 1966), by Zmbov et al. (1968), by Schug and Wagner (1968), and by Carlson (1971). Using equilibrium data in experiments by Farber et al. (1969), one can also determine a value. The heat of formation of :CF2 has also been calculated from the decomposition of various halomethanes: from the decomposition of CHF3 by Schug and Wagner (1978), from the decomposition of CHF2Br by Okafo and Whittle (1974), and from the decomposition of CHF2Cl by Dalby (1964), Gozzo and Patrick (1964), Edwards and Small (1965), and Schug and Wagner (1968). The ionization potential of :CF2 has been used to estimate its heat of formation by Fisher et al. (1965), Pottie (1965), and Zmbov et al. (1968). Various appearance potential measurements by Walter et al. (1969), Berman et al. (1981), and Paulino and Squires (1991) have also been used to estimate a value for the heat of formation of :CF2. The ionization and appearance potential measurements have been reviewed in detail by Lias et al. (1985) and Paulino and Squires (1991).
Thermochemical data for fluoromethylidyne (*CF) can be found in the JANAF tables (Stull and Prophet, 1971). Gurvich et al. (1991) have also provided thermochemical data for *CF. In the latter review, more recent measurements by Hildenbrand (1975) were also considered, in addition to earlier measurements by Modica (1966) and Farber et al. (1969). We used the more recent value from Gurvich et al. (1991) for the heat of formation with the entropy and heat capacity data provided in the JANAF tables. The reported uncertainties in the heat of formation are about 10 kJ/mol. BAC-MP4 calculations yield a heat of formation for *CF (Zachariah et al., 1995) that is within about 10-20 kJ/mol of the recommended literature values.
2.3.4. Carbonyl Fluorides and Fluoromethoxy Radicals
Thermochemical data for the carbonyl fluorides (CHF=O, CF2=O, *CF=O) can be found in the JANAF table. We have employed these data. The uncertainty in the heat of formation of CF2=O is reported to be about 2 kJ/mol. The JANAF recommendation for CF2=O is based upon equilibrium and heat of reaction measurements by Ruff and Li (1939) and von Wartenberg and Riteris (1949). For the other two carbonyl fluorides, where there is little or no experimental data, the estimated uncertainty in their heats of formation are probably at least 15 kJ/mol.
Gurvich et al. (1991) have recommended a value for the heat of formation of *CF=O that is similar to the JANAF recommendation (about 8 kJ/mol higher). This recommendation is based upon appearance potential measurements of McNeil and Thynee (1969) and heat of reaction measurements by Heras et al. (1962).
We find that heats of formation for these species from our BAC-MP4 calculations (Zachariah et al., 1995) are within about 20 kJ/mol of the recommended literature, except for CF2=O, where the calculated value is about 40 kJ/mol higher. Other ab initio calculations (Montgomery et al., 1994; Schnieder and Wallington, 1994) using different approaches also predict a heat of formation for CF2=O that is higher (by about 30 kJ/mol) than the experimental value. Because of this significant difference, both uncertainties in the experimental measurements and ab initio calculations warrant further examination.
The biggest uncertainties here are for CHF=O (+/- 20 kJ/mol) and *CF=O (+/- 10 kJ/mol), where there are little or no direct experimental data available and, consequently, their heats of formation were estimated (Stull and Prophet, 1971) using average bond dissociation energies from other related compounds. Given that reliable experimental data exists for the unimolecular decomposition of CHF=O (Saito et al., 1985), uncertainty in its heat of formation may be unimportant. However, under some conditions the bimolecular reaction *CF=O + H2O => CHF=O + OH (roughly 80 kJ/mol endothermic) may contribute. Consequently, uncertainty in the heat of formation of CHF=O may play some role. In contrast, the heat of formation of *CF=O is very important, since there are not experimental data for its unimolecular decomposition, which is a primary decomposition pathway (competing with H atom combination followed by HF elimination).
We used an experimentally derived value for the heat of formation of the perfluoromethoxy radical CF3O* (Batt and Walsh, 1982) with a reported estimated uncertainty of about 6 kJ/mol. For entropy at standard state and heat capacity data, we used that derived from our BAC-MP4 calculations (Zachariah et al., 1995). The calculated heat of formation of CF3O* is within about 30 kJ/mol of the experimentally derived value.
A number of other species, such as the other fluoromethoxy radicals (CH2FO*, CHF2O*), fluoromethanols (e.g., CF3OH), or fluoromethylperoxy radicals (e.g., CF3OO*), were initially considered in the mechanism (using ab initio thermochemical data). These species were later excluded, because they did not contribute to the overall chemistry. In many cases, these species were present in steady state concentrations and, consequently, the creation and destruction reactions could be combined into a single overall reaction. Although these species may be important in atmospheric chemistry, they are present in extremely low concentrations at high temperatures in hydrocarbon/air flames.
2.4. C2 Fluorinated Hydrocarbons
. . . Goto 2.5.
2.4.1. Fluoroethanes
We chose to use thermochemical data from a Journal of Physical and Reference Data (JPCRD) review (Chen et al., 1975) for the six simple fluoroethanes (CH3-CH2F, CH3-CHF2, CH3-CF3, CH2F-CF3, CHF2-CF3, CF3-CF3). Thermochemical data for the three other fluoroethanes (CH2F-CH2F, CH2F-CHF2, CHF2-CHF2) were obtained from a variety of sources. For CH2F-CH2F, we used a heat of formation calculated using the C-C bond dissociation energy as determined by Kerr and Timlin (1971) and the heat of formation for *CH2F as recommended by McMillen and Golden (1982). We used the heat of formation for CH2F-CHF2 as recommended by Lacher and Skinner (1968). For CHF2-CHF2, we used a heat of formation calculated using the C-C bond dissociation energy as determined by Millward et al. (1971) and the heat of formation for *CHF2 as recommended by McMillen and Golden (1982). Standard state entropy and heat capacities for these other 3 fluoroethanes were computed based on vibrational frequencies and moments of inertia from our ab initio calculations.
We have calculated heats of formation for the fluoroethanes (Zachariah et al., 1995) using the BAC-MP4 method (Melius, 1990) and find the calculated values to be within about 10-20 kJ/mol of the recommended experimental or empirical values in the literature (see Table 4). Three of the fluoroethanes (CH2F-CH2F, CH2F-CHF2, CHF2-CHF2) have conformational isomers. At the MP4/6-31G(d,p)//HF/6-31G(d) level, the trans isomers are slightly more stable (about 4-7 kJ/mol) than the gauche isomers, except for CH2F-CH2F where the energies are within about 0.5 kJ/mol.
We believe some reevaluation of all of the heat of formation data is warranted. For example, the heat of formation of CH3-CF3 recommended in the JPCRD review is based on old values for *CH3 and *CF3. In addition, employing a group additivity scheme with an ionic correction should yield better values for both CH2F-CH2F and CHF2-CHF2 (see discussion below).
There are a number of sources of compiled or evaluated data for the fluoroethanes. Thermochemical data for some of the fluoroethanes can be found in JPCRD (Chen et al., 1975) and the DIPPR compilation (Daubert and Danner, 1985). Recommendations for the heats of formation of some of the fluoroethanes have been made by Kolesov and Papina (1983) and by Pedley et al. (1986). There are no experimentally derived heats of formation for two of the fluoroethanes (CH3-CH2F, CH2F-CF3). These have been estimated using bond additivity, group additivity, or other trends in heats of formation. However, there are significant uncertainties in using these procedures, because of non-covalent or ionic contributions to the stability of these species due to the high electronegativity of fluorine. For example, CH3-CF3 is about 33 kJ/mol more stable than predicted using heats of formation of CH3-CH3 and CF3-CF3. All three of these species have heats of formation that were derived from good quality experimental measurements. The additional stabilization can be rationalized as an ionic contribution to the C-C bond strength because of large differences in net charges on the carbon atoms of the -CH3 and -CF3 groups due to the high electronegativity of the F atoms.
There are a number of different sources of experimental data for the heats of formation of the fluoroethanes. These various sources are described in the paragraphs below.
The heat of formation of ethyl fluoride (CH3-CH2F) has been estimated (Chen et al., 1975) using group additivity and heat of reaction data for propyl fluoride (Lacher et al., 1956). A recommendation for the heat of formation of ethyl fluoride (CH3-CH2F) has also been given by Luo and Benson (1988) based on electronegativity correlations of heats of formation of substituted alkanes. This recommendation is significantly lower (15 kJ/mol) than other recommendations. This significant difference warrants further examination. CH3-CH2F is unlikely to be important as a species in the fluorocarbon-inhibited hydrocarbon flames. However, as a simple, single-substituted fluorinated hydrocarbon (like CH3F), its heat of formation is important as a reference point for the heats of formation of other species. For example, another -CH2F substituted fluoroethane, CH2F-CF3, has no experimentally derived heats of formation. Any uncertainties in the heats of formation and, consequently, stability of the fluoroethanes may influence product channels for fluoromethyl combinations (e.g., *CH3 + *CF3 => CH3-CF3 versus *CH3 + *CF3 => CH2=CF2 + HF).
4olesov et al. (1968) have measured the heat of combustion of CH3-CHF2, from which one can calculate its heat of formation. The heat of formation of CH3-CHF2 could be determined from the enthalpy of hydrogenation of CF2=CCl2 as measured by Lacher et al. (1956) given a reliable value for the heat of formation of CF2=CCl2 could be obtained.
We calculated a heat of formation for CH2F-CH2F based on the C-C bond dissociation energy (368.6 kJ/mol) as determined by Kerr and Timlin (1971) and the heat of formation for *CH2F (-32.6 kJ/mol) as recommended by McMillen and Golden (1982). The bond dissociation energy was determined from the critical energy (E0) calculated using RRKM analysis of experimental kinetic data for thermal (Chang and Setser, 1969) and chemically activated decomposition of CH2F-CH2F.
Kolesov et al. (1965) have determined a heat of formation for CH3-CF3 by measuring its heat of combustion. Kinetic data for the forward and reverse reactions for *CH3 + *CF3 => CH3-CF3 can be used to obtain a heat of formation for 1,1,1-trifluoroethane. Kinetic data for this reaction have been obtained by Giles and Whittle (1965), Pritchard and Perona (1970), and Chang et al. (1972). These data have been reviewed by Rodgers and Ford (1973).
The heat of formation of CH2F-CHF2 has been determined (Kolesov and Papina, 1983) from the enthalpy of hydrogenation of CF2=CFCl as measured by Lacher et al. (1956).
We have calculated a heat of formation for CHF2-CHF2 based on the C-C bond dissociation energy (382.4 kJ/mol) as determined by Millward et al. (1971) and the heat of formation for *CHF2 (-247.7 kJ/mol) as recommended by McMillen and Golden (1982). The bond dissociation energy was set equal to the activation energy for thermal decomposition of CHF2-CHF2, which was determined from analysis of experimental kinetic data.
The heat of formation of CHF2-CF3 can be obtained from equilibrium data with CF3-CF2Br (and group additivity) as measured by Whittle and coworkers (Coomber and Whittle, 1967; Ferguson and Whittle, 1972) and from heat of reaction data for the bromination of CF2=CF2 (and group additivity) as measured by Lacher et al. (1956). In addition, one can calculated a value for the heat of formation for CHF2-CF3 from the heat of formation of the perfluoroethyl radical (CF3-CF2*) and the CF3CF2-H bond dissociation energy. Wu and Rodgers (1976) determined the heat of formation of the perfluoroethyl radical by measuring the enthalpy of its reaction with I2. Values for the bond dissociation energy of CF3CF2-H have been determined by Bassett and Whittle (1972) and Martin and Paraskevopoulos (1983).
The heat of formation of CF3-CF3 has been determined from equilibrium data with CF3Br as measured by Coomber and Whittle (1967), with CF3-CN as measured by Walker et al. (1970), and with CF4 (and NF3 as the oxidizer) as measured by Sinke (1966).
2.4.2. Fluoroethyl Radicals
In the absence of reliable experimental data, we used the calculated thermochemical data for the fluoroethyl radicals as provided by Tschuikow-Roux and coworkers (Chen et al., 1990, 1991) for consistency. However, we believe some reevaluation of all of the heat of formation data (both experimental and ab initio) is warranted. For the radical CH3-CHF*, we used the average of the heats of formation reported by Martin and Paraskevopoulos (1983) and Tschuikow-Roux and Salomon (1987). For the three fluoroethyl radicals, CH2F-CHF*, CHF2-CF2*, and CF3-CHF*, we calculated heats of formation based on C-H bond dissociation energies determined by Martin and Paraskevopoulos (1983). We note that heats of formations for the fluoroethyl radicals from our BAC-MP4 ab initio calculations (Zachariah et al., 1995) are within about 10-20 kJ/mol of the recommended literature values (see Table 4).
There are a number of sources of heats of formation for the fluoroethyl radicals. There are experimentally derived thermochemical data (Rodgers, 1978) for only three of the fluoroethyl radicals (CH3-CF2*, CF3-CH2*, CF3-CF2*). Heats of formation for the others have been estimated using heats of formation for the fluoroethanes and C-H or C-F bond dissociation energies for CH3-CHF* and CF3-CHF* by Martin and Paraskevopoulos (1983), for CH3-CHF* by Tschuikow-Roux and Salomon (1987), and for all of the other fluoroethyl radicals in this work (see Table 4). Thermochemistry for all of the fluoroethyl radicals have been calculated using ab initio molecular orbital theory by Tschuikow-Roux and coworkers (cited above). They used the experimentally derived heats of formation of the 3 fluoroethyl radicals recommended by Rodgers (1978). For the others, they used their calculated energies in conjunction with isodesmic-homodesmic reactions (with known experimental reaction enthalpies) to provide values that approach the "true" heats of formation.
2.4.3. Fluoroethylenes and Fluorovinyl Radicals
There are six fluoroethylenes (CH2=CHF, CH2=CF2, CHF=CHF[Z], CHF=CHF[E], CHF=CF2, CF2=CF2), including the configurational isomers. In order to reduce the number of species in the reaction set, we use only the Z isomer of CHF=CHF, which is only slightly more stable (~1-4 kJ/mol).
We used the heat of formation of CH2=CHF as recommended by Gurvich et al. (1991). Entropy at standard state and heat capacity data were taken from the DIPPR compilation (Daubert and Danner (1985). These data can also be found in the TRC Thermodynamic Tables (1990). The heat of formation data are based on measurements by Kolesov and Papina (1970) of the heat of combustion of vinyl fluoride. Pedley et al. (1986) have also made a recommendation based on this experimental data. A heat of formation was also determined by Williamson et al. (1976) based on appearance potential measurements.
We have chosen to use heats of formation for CHF=CHF[E] and CHF=CHF[Z] based on appearance ionization potential measurements by Stadelman and Vogt (1980) and entropies at standard state and heat capacities based on geometries and vibrational frequencies from our BAC-MP4 ab initio calculations (Zachariah et al., 1995). Gurvich et al. (1991) have also estimated heats of formation for these species using a bond additivity method. For CH2=CF2, we used the heat of formation recommended by Gurvich et al. (1991) with entropy at standard state and heat capacity data taken from Stull et al. (1969). Recommendations for the heat of formation for 1,1-difluoroethylene have also been made by Lacher and Skinner (1968), Stull et al. (1969), Cox and Pilcher (1970), and Pedley et al. (1970). All of these recommendations are based on heat of combustion measurements by Neugebauer and Margrave (1956) and Kolesov et al. (1962).
We used thermochemical data for CHF=CF2 as recommended by Gurvich et al. (1991). The heat of formation data is based on an experimental measurement by Kolesov et al. (1962) of the heat of combustion of trifluoroethylene. Recommended values (also based on these experiments) can be found in the evaluations of Stull et al. (1969), Cox and Pilcher (1970), and Pedley et al. (1986).
We used thermochemical data for CF2=CF2 from the JANAF tables (Stull and Prophet, 1971). The recommended heat of formation is based the heat of reaction data for conversion to amorphous carbon by Neugebauer and Margrave (1956) and Kolesov et al. (1962). Lacher and Skinner (1968), Stull et al. (1969), Cox and Pilcher (1970), Kolesov and Papina (1983), Pedley et al. (1986), and Gurvich et al. (1991) have all reviewed the existing experimental data and made recommendations. These evaluations were made based upon a number of different sources of experimental heat of reaction data for perfluoroethylene, including the data of Lacher et al. (1949), Lacher et al. (1950), Kirkbride and Davidson (1954), von Wartenberg and Schiefer (1955), Duus (1955), Neugebauer and Margrave (1956), Lacher et al. (1956), Scott et al. (1956), Kolesov et al. (1962), and Edwards and Small (1964).
We note that the heats of formation for the fluoroethylenes that we have calculated using the BAC-MP4 ab initio method are within about 10 kJ/mol of the recommended experimental values (see Table 4). At the MP4/6-31G(d,p)//HF/6-31G(d) level, the CHF=CHF[Z] isomer is about 0.9 kJ/mol more stable than the E form.
There are seven fluorovinyl radicals (CHF=CH*[Z], CHF=CH*[E], CH2=CF*, CHF=CF*[Z], CHF=CF*[E], CF2=CH*, CF2=CF*), including the configurational isomers. In order to reduced the number of species in the reaction set, we used only the Z isomers which are only slightly more stable (~1-2 kJ/mol).
There are not any experimentally derived thermochemical data (to our knowledge) for the fluorovinyl radicals, other than the heat of formation for CF2=CF*. The heat of formation of the perfluorovinyl radical has been estimated by Bryant (1962) based on trends in C-F bond dissociation energies for perfluorocarbons. Gurvich et al. (1991) recommended a value based on a review of appearance potential measurements by Thynee and MacNeil (1970), Lifshitz and Crajower (1972), and Bibby and Caster (1966). Because of the lack of experimental data for most of the fluorovinyl radicals, we chose to use thermochemical data from our BAC-MP4 ab initio calculations (Zachariah et al., 1995) in order to provide a consistent set. We note that our calculated value is within about 10 kJ/mol of the experimentally derived value that was recommended by Gurvich et al. (1991). At the MP4/6-31G(d,p)//HF/6-31G(d) level, the CHF=CH*[Z] and CHF=CF*[Z] isomers are about 1.3 and 1.7 kJ/mol, respectively, more stable than the E forms.
2.4.4. Fluoroethynes, Fluoroketenes, and Fluoroketyl Radical
Data on the thermochemistry of the fluoroethynes (C2HF, C2F2) can be found in the JANAF tables (Stull and Prophet, 1971), however, with relatively large uncertainties: +/- 60 kJ/mol and +/- 20 kJ/mol in the heats of formation, respectively. Fluoroketenes (CHF=C=O and CF2=C=O) and the fluoroketyl radical (*CF=C=O) can be formed through a number of channels. These channels are analogous to those considered in pure hydrocarbon chemistry for ketene (CH2=C=O). To assess the importance of the fluoroketene species and relevant reactions, we included these species in the mechanism. There are not any experimentally derived data for these species. Consequently, we used data from our BAC-MP4 ab initio calculations (Zachariah et al., 1995).
A number of other partially oxidized species, such as CH3-CFO, were excluded from the mechanism based on the assumption that they would be only present in steady state concentrations at flame temperatures. For lower temperatures, these species may become important and, consequently, our assumption should be reevaluated. It is possible that perfluoro-oxidized species, such as CF3-CFO, may be present at flame temperatures. For example, since both *CF3 and *CFO are present in significant concentrations, the combination of these species (and stabilization) may be a source of CF3-CFO. This should be examined in future refinements of this mechanism.
For a number of species considered in the reaction set, especially the radicals, there are little or no thermochemical data. Consequently, we have estimated that data using BAC-MP4 ab initio calculations (see description below). In order to quantify the uncertainties in the calculated data, we have also performed calculations on many related species where there is good quality experimental data.
Structures, energies, and thermochemical data for a large number of C1 and C2 hydrocarbons, oxidized hydrocarbons, hydrofluorocarbons, and oxidized hydrofluorocarbons, including radical species, were calculated using the BAC-MP4 procedure as outlined by Melius (1986). This procedure involves ab initio molecular orbital calculations using the Gaussian series of programs (Frish et al., 1990), followed by application of a bond additivity correction (BAC) procedure to the ab initio calculated energies. The BAC procedure enables energies to be calculated at accuracies that are necessary for chemical applications, without the need to resort to large basis sets or configuration interaction terms. This is a particularly important issue when the goal is the generation of a sufficiently complete data set necessary for development of a detailed chemical mechanism.
Equilibrium geometries, vibrational frequencies, and zero point energies were calculated at the Hartree-Fock level using a 6-31G(d) basis set (HF/6-31G*). Using these geometries, single point energies were calculated with 4th order Moller-Plesset theory using a 6-31G(d,p) basis set (MP4/6-31G**), to which the BAC procedure was applied. In the BAC method, errors in the electronic energy of a molecule are bond-wise additive and depend on bonding partner, distance, and next-nearest neighbors. The energy per bond is corrected by calibration at a given level of theory against molecules of known energy.
Table 4 lists calculated heats of formation for most of the species in the reaction set, as well as literature values (where available). We note that we have calculated thermochemical data for a number of related species that are not included in the reaction set. These data are also included in Table 4 for purposes of comparison. Of the approximately 110 species, where we have calculated heats of formation, about 70 species have literature values. We note that the literature values consist of a number of different types of data, including estimated and calculated values, in addition to those that are derived from experimental measurements.
The average difference between the BAC-MP4 and the literature values is about 9.5 kJ/mol, while the standard deviation is about 7.5 kJ/mol. From these data, we conclude that for the fluorinated hydrocarbon system, that heats of formation calculated using the BAC-MP4 method provide values that are accurate to less than 10 kJ/mol or comparable to the majority of the experimentally derived values. We believe that the precision of the ab initio values for any homologous series to be significantly better than that which is typically obtainable from experimental measurements. This becomes evident when calculated bond dissociation energies are compared to those derived from experimental measurements. A more detailed discussion and comparison can be found elsewhere (Zachariah et al., 1995).
Of all the species, CF2=O has the largest difference between calculated and experimental values. Although the quoted uncertainty for this molecule is small, there is reason to believe that the experimental data may have had side reactions complicating its determination. In addition, other recent calculations (Schnieder and Wallington, 1994; Montgomery et al., 1994) using other ab initio methods predict a heat of formation for CF2=O that is consistent with our BAC-MP4 calculated value. There are a number of other oxyfluoro-species that have significant differences between calculated and literature values. However, the heats of formation of these species were derived based on heats of reactions involving CF2=O. Consequently, if the "true" value for CF2=O was closer to the calculated value, then the experimentally derived values for these other species would also be closer to their respective calculated values.
There are a number of other species with significant differences between calculated and literature values. The uncertainties in many of these literature values are high because they are only indirectly tied to experimental measurements. For example, the heat of formation of the HCOO* radical is an estimate based on group additivity. The heats of formation of two fluoroethyl radicals (CF3-CHF* and CH2F-CF2*) were determined from estimated from C-H bond dissociation energies based on correlations between rates of H atom abstractions, C-H bond frequencies, and known C-H bond strengths.
To reiterate, from analysis of the data presented in Table 4, we can conclude that for the fluorinated hydrocarbon system, that heats of formation calculated using the BAC-MP4 method provide values that are accurate to less than 10 kJ/mol or comparable in accuracy to the majority of the experimentally derived values. Furthermore, from trends in bond dissociation energies, we believe that the precision of the ab initio values for any homologous series to be significantly better than that which is typically obtainable from experimental measurements.
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