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Shock Wave Study of the Thermal Decomposition of CF3 and CF2 Radicals† C. J. Cobos,‡,§ A. E. Croce,‡,§ K. Luther,§,| and J. Troe*,§,| INIFTA, Facultad de Ciencias Exactas, UniVersidad Nacional de La Plata, Argentina, Max-Planck-Institut fu¨r Biophysikalische Chemie, Am Fassberg 11, D-37077 Go¨ttingen/Germany, and Institut fu¨r Physikalische Chemie, UniVersita¨t Go¨ttingen, Tammannstrassse 6, D-37077 Go¨ttingen/Germany ReceiVed: September 24, 2009; ReVised Manuscript ReceiVed: NoVember 24, 2009
The thermal dissociation reactions CF3 + M f CF2 + F + M (reaction 1) and CF2 + M f CF + F + M (reaction 3) were studied behind shock waves. CF2 radicals were monitored through their UV absorption. By working at very low reactant concentrations, the rate coefficients of the unimolecular processes could be derived. Reaction 1 was investigated between 1600 and 2300 K in the intermediate range of the falloff curves, at ∼10 times larger bath gas pressures than employed in earlier work (Srinivasan, N. K.; Su, M.-C.; Michael, J. V.; Jasper, A. W.; Klippenstein, S. J.; Harding, L. B. J. Phys. Chem. A 2008, 112, 31). The combination of the two sets of data, together with theoretical modeling, allows one to construct falloff curves and to provide complete representations of the temperature and pressure dependences of the rate coefficients. Reaction 3 was studied in the limiting low-pressure range and, over the range 2900-3800 K, a rate coefficient k3 ) [Ar] 1.6 × 1015 exp(-48 040 K/T) cm3 molecule-1 s-1 was obtained. Representations of the rate coefficients over the full falloff curves were again derived by theoretical modeling. 1. Introduction The thermal dissociation of CF3 is an important step in the high-temperature pyrolysis of fluor-containing compounds such as C2F6 or CF3X, where X is a halogen. It was first studied in ref 1, where CF3 radicals were formed in shock waves alternatively by thermal dissociation of C2F6 or CF3I and the progress of the reaction was followed through observation of the UV absorption at 266 nm of the forming CF2 radicals. Assuming that the reaction
CF3 + M f CF2 + F + M
(1)
is in the low pressure limit for the applied bath gas concentrations ([M] ) [Ar] ) (0.8 to 1.1) × 10-5 mol cm-3), a pseudofirst-order rate constant k1 ) [Ar] 1.57 × 1049 T-9.04 exp(-46 425 K/T) cm3 mol-1 s-1 was derived over the temperature range 1740-2210 K. The evaluation of the kinetics was somewhat hampered by the possibility of secondary reactions such as
F + CF3 + M f CF4 + M
(2)
occurring under the relatively high concentrations of the experiments (1% of C2F6 or CF3I in M ) Ar). High concentrations also were found to be responsible for nonisothermal shock wave conditions. Much lower reactant concentrations were employed in a more recent shock wave study,2 which consequently led to more reliable results. In this case, again, the dissociation of CF3I was used as the source of CF3 radicals. However, in contrast with ref 1, the formation of F atoms by reaction 1 was followed †
Part of the special section “30th Free Radical Symposium”. * Corresponding author. E-mail:
[email protected]. ‡ Universidad Nacional de La Plata. § Max-Planck-Institut fu¨r Biophysikalische Chemie. | Universita¨t Go¨ttingen.
through the sensitive detection of OH radicals formed by the fast reaction F + H2O f HF + OH in the presence of added H2O. By this technique, reactant concentrations relative to M ) Kr could be decreased to (3-6) × 10-5. Bath gas concentrations of (2-6) × 10-6 mol cm-3 and temperatures in the range of 1800-2200 K were applied. The derived rate constants k1 ) [Kr] 2.78 × 1015 exp(-30020 K/T) cm3 mol-1 s-1 were found to be factor of 2 to 2.5 smaller than those of ref 1. The discrepancy was attributed to complications related to the high reactant concentrations and unfavorable shock wave conditions applied in ref 1. Modeling by unimolecular rate theory of the rate constant k1 in ref 2 led to limiting low-pressure rate constants k1,0 ) [Kr] 2.38 × 1024 (T/298 K)-6.362 exp(-45 649 K/T) cm3 mol-1 s-1, limiting high-pressure rate constants k1,∞ ) 1.27 × 1016 (T/298 K)-0.868 exp(-43 186 K/T) s-1, and falloff curves with temperature-independent center broadening factors Fcent ) 0.27 over the range 1300-2500 K. On this basis, it was estimated that the measured k1 from ref 2 corresponds to only moderate deviations from the low pressure limit, but that deviations from the low pressure limiting k1,0 at [Kr] ≈ 10-6 mol cm-3 nevertheless should still be on the order of ∼20%. In this situation, we felt that measuring k1 at different bath gas concentrations would improve the construction of the falloff curve of reaction 1 and the conclusions on k1,0 and k1,∞. As a matter of fact, the modeling of low-pressure rate constants today still has to use the average energies transferred per collision and the corresponding collision efficiencies as free fit parameters whose properties can only be estimated semiquantitatively. Whereas the modeling of k1,∞ in ref 2 was based on advanced ab initio calculations of the potential energy surface of CF3 and thus appears to be fairly reliable, the modeling of k1,0 for the mentioned reasons could only be approximate. For this reason, obtaining experimental information on larger parts of the falloff curves appeared desirable. This is the subject of the present study in which about 10 times larger bath gas concentrations were employed than in ref 2. Whereas the reaction was followed by
10.1021/jp9091877 2010 American Chemical Society Published on Web 01/04/2010
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observing the UV absorption of CF2 like in ref 1, the employed reactant concentrations were markedly lower than those in ref 1 such that more suitable conditions could be realized. By combining experimental data along the falloff curve with semiquantitative modeling, suitable expressions for the complete pressure and temperature dependences of k1 can be derived. Using the decomposition of C2F6, followed by reaction 1 as a way to produce CF2 radicals, one may also study the thermal dissociation of CF2
CF2 + M f CF + F + M
(3)
Whereas CF4, CF2, and CF all have C-F bond energies >500 kJ mol-1, that of CF3 is only 358 kJ mol-1. Therefore, much higher temperatures than those for reaction 1 need to be applied for studying reaction 3. Besides generating CF2 from C2F6 or CF3I dissociation, followed by reaction 1, one also may use other CF2 precursors. In our work, besides C2F6, we also used the thermal dissociations C2F4 f 2 CF2 and CF3H f CF2 + HF for this purpose. In contrast with the temperature range 1600-2300 K of our study of CF3 decomposition (1), temperatures of 2900-3800 K had to be used for studying reaction 3. Under typical shock wave conditions, this reaction then is very close to the low pressure limit. We again applied unimolecular rate theory to model k3, and we compared the results with those obtained for reaction 1. To our knowledge, the only previous study of reaction 3 is that from ref 3, in which the bath gas M also was Ar, temperatures were in the range of 2600-3700 K, and bath gas concentrations were ∼2 × 10-6 mol cm-3. k3 was measured as k3 ) 4.2 × 1026 T-2.85 exp(-53340 K/T) cm3 mol-1 s-1. Similar to our work, CF2 was followed by its UV absorption at 253.6 nm. However, again, relatively high precursor concentrations (1% of C2F4 in Ar) were employed such that nonisothermal conditions were realized and the decomposition at the employed concentrations was not complete because of the approach of an equilibrium. Alerted by the discrepancies between refs 1 and 2 for reaction 1, we felt that remeasuring k3 at much lower reactant concentrations than those employed in ref 3 would also be desirable. Such experiments are also described in the present work.
Figure 1. Absorption-time profile of CF2 formed by dissociation of CF3 (produced by fast dissociation of the precursor C2F6) behind reflected shock wave (T ) 1610 K, [Ar] ) 7.2 × 10-5 mol cm-3, [CF3]0 ) 4.0 × 10-8 mol cm-3).
We followed the absorption signal of CF2 at 248 nm, using a high-pressure Xe lamp as light source and recording the absorption signal after single passage of the light beam through the shock tube (10 cm inner diameter). Figure 1 shows a typical absorbance-time profile for experiments near 1600 K. The two schlieren peaks indicate the passage of the incoming and the reflected shock at the observation window. Behind the reflected shock, the CF2 absorption gradually increases with time. The drop of the signal after 1.5 ms indicates that the onset of
2. Experimental Technique and Results In the present work, the dissociation of CF3 radicals was studied in reflected shock waves using C2F6 as the precursor for CF3. For the highest temperatures of our work, the dissociation of C2F6 was sufficiently fast to act as an almost instantaneous source of CF3, whereas the reverse recombination of CF3 radicals to C2F6 practically did not take place. The rate coefficients for dissociation of C2F6 were obtained from studies of the reverse recombination of CF3 radicals between 300 and 1300 K and the equilibrium constant. (See refs 4–6 and work cited therein.) For the lowest temperatures of our work, besides the dissociation of C2F6, the reverse recombination of CF3 (and other reactions) also had to be taken into account. As the temperature dependence of the dissociation of CF3 was well studied in ref 2, our present work concentrated on measurements at two temperatures only, namely, at the high temperature end of our range of CF3 studies, at 2150-2300 K, and at the low temperature end at 1600-1650 K. For these two temperatures, we then focused on measurements at higher bath gas pressures than those used in ref 2. Our shock tube and the applied technique have been previously described7,8 and do not need to be characterized here again.
Figure 2. (a) As Figure 1, but at higher temperature (T ) 2160 K, [Ar] ) 4.7 × 10-5 mol cm-3, [CF3]0 ) 5.0 × 10-8 mol cm-3). (b) As Figure 2a, but with expanded time scale.
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perturbations such as this is typical for the described type of shock wave experiments. Therefore, only reaction times up to ∼1 ms could be safely evaluated. The value of the decadic absorption coefficient, ε, of CF2 at 248 nm and its temperature dependence has been measured in ref 9, confirming the results from ref 10. The latter reference also summarized earlier measurements and provided a consistent picture of the wavelength and temperature dependence of ε. We used a value of ε(CF2) ) 1.5((0.1) × 106 cm2 mol-1. Figure 2a,b illustrates an example of experiments near 2200 K. Figure 2a displays the absorption signal up to 800 µs in which the CF2 absorption first rises and then falls until a final level is reached. Figure 2b provides a better resolution of the rise time, the initial shoulder of the signal being due to the schlieren peak and facilitating the identification of the time zero of the reaction behind the reflected shock. The recorded absorbance signals of Figure 2a,b have already been converted to relative concentrations [CF2]/ [C2F6]0. This ratio does not reach a value of 2, and the CF2 concentration decreases after reaching a maximum, which indicates that the mechanism is not only characterized by reaction 1 but also shows the effects of secondary reactions, as described in the following. To evaluate absorption-time profiles such as those shown in Figures 1 and 2, only a small number of reactions have to be taken into account. At temperatures near 1600 K, the primary dissociation of the CF3-precursor C2F6
(4)
C2F6(+M) f 2 CF3(+M) and the reverse recombination of CF3 radicals
(-4)
establish an equilibrium reservoir of CF3 radicals that is then depleted by reaction 1. Following this, the reaction of the forming F atoms with CF3 through reaction 2 may lead to the stable product CF4, but the reverse of reaction 1, that is
CF2 + F + M f CF3 + M
(-1)
also has to be considered. At temperatures near 2200 K, the dissociation of C2F6 is very rapid and approaches nearly complete conversion of C2F6 into 2CF3. The formation of CF2 then is dominated by reaction 1. In addition, its reverse reaction -1 competes with the formation of the stable product CF4 through reaction 2. As a result, the ratio [CF2]/[C2F6]t)0 does not reach up to a value of 2. (One should note that the CF4 concentration is given by the balance [CF4] ) 2 [C2F6]t)0 - [CF2] - [CF3]). After reaching a maximum, the CF2 concentration decreases, such as illustrated in Figure 2a. This indicates that some further reactions take place TABLE 1: Examples for Rate Coefficients of CF3 Dissociation and Experimental Conditions (See the Text) 1610 1645 2160 2175 2175 2230 2270
[Ar]/mol cm-3 -5
7.2 × 10 7.0 × 10-5 4.7 × 10-5 4.7 × 10-5 4.8 × 10-5 4.6 × 10-5 4.4 × 10-5
[C2F6]0/mol cm-3 -8
2.0 × 10 3.7 × 10-8 2.5 × 10-8 2.3 × 10-8 2.5 × 10-8 2.4 × 10-8 9.3 × 10-8
quantity
rate coefficients
k1/[Kr] k1/[Ar] k2/[Ar] k3/[Ar] k-4
2.8 × 10 exp(-30 020 K/T) 5.2 × 1014 exp(-28 200 K/T) 6.36 × 1016 (T/2000 K)-8.552 1.6 × 1015 exp(-48 040 K/T) 7.8 × 1012
k1/k-1 k4/k-4
15
k1/[Ar] cm3 mol-1 s-1 1.5 × 107 1.6 × 107 1.0 × 109 1.7 × 109 1.5 × 109 1.0 × 109 2.0 × 109
ref a
2 this workb 1, 27 this work 4, 5c
Equilibrium Constants (at 1600-3000 K) 34 exp(-42 000 K/T) 27 25.3 exp(-40 400 K/T) 6
a [Kr] ) (2-6) × 10-6 mol cm-3. b [Ar] ) (4-7) × 10-5 mol cm-3. c Accounting for the relevant falloff effects.
after most of the reaction is over. We are not in a position to identify uniquely all of these processes. There may be the slightly exothermic reaction of CF2 with some remaining CF3
CF2 + CF3 f CF + CF4
(5)
or some endothermic reactions of remaining F with CF2, characterized by the sequence
F + CF2 f F2 + CF f 2F + CF
(6)
possibly followed by
F + CF + M f CF2 + M
2 CF3(+M) f C2F6(+M)
T/K
TABLE 2: Rate Coefficients (in cm3 mol-1 s-1) and Equilibrium Constants (in mol cm-3) Used in the Modeling (See the Text)
(-3)
The thermal dissociation of CF2 is too slow to be of importance under the conditions of the experiments near 2200 K. (See below.) Likewise, the combination of 2 CF2 radicals to form C2F4 is too slow to explain the observed profiles. Reactions 5 and 6 do not perturb the analysis of the rise of the CF2 signals to a major extent. Nevertheless, the accuracy of the determination of k1 is slightly influenced by the presence of secondary reactions like 5, 6, and -3. We fitted an empirical rate constant for such reactions from the observed CF2 decays to account for their presence in the essential period of CF2 formation at earlier times. The combined statistical and systematic error of our determination of k1 is estimated to be (30%. It should be emphasized that the secondary reactions neither near 1600 K nor near 2200 K influence the evaluation of the rise time of CF2 to a major extent. However, including the complete mechanism of secondary reactions, which we attempted, somewhat improves the accuracy of the results. Table 1 presents a selection of experimental conditions and rateconstantsk1 derivedinthepresentwork.Theconcentration-time profiles were fitted with the set of rate constants summarized in Table 2. However, the sensitivity against k1 was always dominant. Our resulting values for k1/[Ar] ) 1.5 × 107 cm3 mol-1 s-1 at 1625 ((20) K and [Ar] ) 7.1 × 10-5 mol cm-3 and k1/[Ar] ) 1.4 × 109 cm3 mol-1 s-1 at 2200 ((70) K and [Ar] ) 4.6 × 10-5 mol cm-3 later on are compared with the data from ref 2, which were obtained at markedly lower pressures. In this way, two falloff curves, one near 1625 K and one near 2200 K, were obtained. Before moving on to our results for the dissociation of CF2 radicals, we illustrate complete kinetic modeling of experiments such as that characterized in Table 1 by employing the set of rate constants from Table 2. Figures 3 and 4 illustrate two typical
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Cobos et al. TABLE 3: Examples for Rate Coefficients of CF2 Dissociation and Experimental Conditions (See the Text)
Figure 3. Modeling of concentration-time profiles for CF3 formation and decay as well as CF2 formation (T ) 1610 K, conditions of Figure 1; [C2F6] ) curve 1, [CF3] ) curve 2, [CF2] ) curve 3, [F] ) curve 4; rate constants from Table 2; curve 4 coincides with the horizontal axis).
Figure 4. As Figure 3 (T ) 2160 K, conditions of Figure 2a,b; curve 1 coincides with the vertical axis).
examples of modeled concentration-time profiles. The CF2 profiles calculated correspond to those measured and illustrated in Figures 1 and 2. Most of our experiments studying the dissociation of CF2 used C2F4 as the precursor, but the results also agreed with those
Figure 5. Absorption-time profile of CF2 formed by dissociation of C2F4 behind incident shock wave and dissociating behind reflected shock wave (T ) 3170 K, [Ar] ) 4.8 × 10-5 mol cm-3, [CF2]0 ) 2, [C2F4]0 ) 2.8 × 10-8 mol cm-3).
T/K
[Ar]/mol cm-3
[C2F4]0/mol cm-3
k3/[Ar] cm3 mol-1 s-1
2900 2950 3014 3170 3175 3310 3320 3330 3510 3550 3625 3670 3755 3780
5.4 × 10-5 5.3 × 10-5 5.0 × 10-5 4.6 × 10-5 4.9 × 10-5 2.5 × 10-5 4.6 × 10-5 2.5 × 10-5 2.2 × 10-5 2.2 × 10-5 3.6 × 10-5 4.2 × 10-5 3.6 × 10-5 3.3 × 10-5
8.1 × 10-9 7.8 × 10-9 7.5 × 10-9 7.0 × 10-9 7.3 × 10-9 1.8 × 10-9 3.4 × 10-9 1.9 × 10-9 1.6 × 10-9 1.6 × 10-9 3.0 × 10-9 3.0 × 10-9 3.0 × 10-9 2.8 × 10-9
6.5 × 107 1.6 × 108 2.0 × 108 4.3 × 108 3.5 × 108 1.0 × 109 9.3 × 108 1.3 × 109 1.8 × 109 2.6 × 109 3.0 × 109 2.3 × 109 4.2 × 109 3.9 × 109
from other precursors such as C2F6 and CF3H. We employed the same shock wave technique as that described above for the decomposition of CF3. However, now initial concentrations [C2F4]0/[Ar] as low as 100 ppm were employed, being 100 times lower than used in ref 3. The precursor C2F4 decomposed completely behind the incident shock such that a mixture of ∼200 ppm of CF2 and Ar was heated in the reflected shock. Figure 5 shows a typical CF2 absorption-time profile for this type of experiment. The formation of CF2 behind the incident wave was found to be consistent with the known rate of decomposition of C2F4 (see, for e.g., refs 5, 9, and 10) and is not further analyzed in the present article. The subsequent decomposition of CF2 behind the reflected wave follows a firstorder rate law down to nearly complete consumption of CF2. The small residual absorption of a few percent of the initial CF2 signal partially corresponds to the CF2 S CF + F equilibrium, and because of its small magnitude, it does not need to be further taken into consideration. Experiments like that of Figure 5 were made for temperatures behind the reflected shock between 2900 and 3800 K and for [Ar] near 5 × 10-5 mol cm-3. No deviations from a proportionality between [Ar] and the pseudo-first-order decay constants k3 were observed. Measured second-order rate constants k3/[Ar] in Table 3 are summarized together with the experimental conditions. They are plotted in an Arrhenius representation in Figure 6. A fit to our results is given by
Figure 6. Low-pressure rate coefficients of the dissociation CF2 + Ar f CF + F + Ar.
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k3 ) [Ar] 1.6 × 1015 exp(-48 040 K/T) cm3 mol-1 s-1 (7) The results from ref 3 are a factor of four larger than the present results. This discrepancy can be traced back to a number of complications encountered in the experiments from ref 3 and related to the high reactant concentrations employed. First, the high concentrations were responsible for nonisothermal reaction conditions, which were difficult to account for. Second, similar to reaction -3, which leads to the establishment of an equilibrium with reaction 3, reaction 6 will also play a role at high concentrations. Because typically only about one half of the initial CF2 disappeared in the experiments of ref 3, both reactions -3 and 6 will have complicated the approach of the equilibrium. Working at much lower concentrations circumvents these problems. The present results of eq 7, therefore, supersede the older results from ref 3. The low concentrations employed in our work also had the advantage that reactions of fluorine atoms from the dissociation of CF2 (or from the slower dissociation of CF) with CF2 or CF could be neglected. The absence of major residual absorption in Figure 5 confirms this modeling result. 3. Theoretical Modeling: Methodology and Results 3.1. Low-Pressure Rate Constants. Modeling of the lowpressure rate constants k1,0 and k3,0 can be done within the framework of unimolecular rate theory such as that outlined in refs 11 and 12. As emphasized above, the unknown average energy transferred per collision (or down transferred per down-collision) remains a fit parameter derived from the experimental collision efficiencies βc ) k/k0SC, where k0SC denotes strong collision rate constants. Analytical solutions of the master equation in ref 12 provided relationships between βc and (or down) given by
βc ≈
(
down down + FEkT
)
2
2 ≈ -down /(down + FEkT)
βc/(1 - β1/2 c ) ≈ - /FEkT
(8)
(9) (10)
where FE is a factor close to unity accounting for the energy dependence of the vibrational density of states.11,12 Equations 8-10 are useful when results from numerical solutions of the master equation for a given down, such as performed in ref 2, are compared with the simpler analytical solutions of the master equation given by eqs 8-10. This will be done below. The determination of experimental collision efficiencies, βc, requires the calculation of strong collision rate constants, k0SC, as described in refs 11 and 12. This calculation, however, leaves some uncertainties because several molecular properties are not well known. Among these are anharmonicities, centrifugal barriers, and so on. Unfortunately, these were not specified in detail for the modeling of k1,0 done in ref 2. However, the value for down was given as down ) hc(200 cm-1) (T/300 K)0.85 such that from the experimental and modeled k1,0 ) [Kr] 2.38 × 1024 (T/298 K)-6.362 exp(-45 649 K/T) cm3 mol-1 s-1 10 3 -1 with eq 8 a value of kSC 1,0(2200 K) ) [Kr] 5.47 × 10 cm mol -1 s can be reconstructed. Following ref 11, we have modeled SC k1,0 ourselves using the molecular parameters given in the SC (2200 K) ) [Kr] 3.39 × 1010 cm3 Appendix. We obtained k1,0
mol-1 s-1. The difference against the results from ref 2 partially is due to the difference of the used bond energies (∆H0o ) 357.7 kJ mol-1 in this work from refs 6 and 13 and ∆H0o ) 352.3 kJ mol-1 from ref 2), partially different molecular frequencies were employed (experimental frequencies for CF3 from ref 14 and for CF2 from refs 15 and 16 in this work and quantum chemical calculations in ref 2), partially different anharmonicities and rotational factors must have been used as well. The agreement SC within roughly a factor of two, in view of of the modeled k1,0 the many uncertainties of the modeling, nevertheless appears encouraging, although some compensation of differences in the contributions must also have happened. The difference in the SC in comparison with the experiments finally is modeled k1,0 compensated by the fitted values for or down, for example, with down, as used in ref 2, one would have SC - ≈ hc 360 cm-1 at 2200 K, whereas our modeled k1,0 with the measured k1,0 of ref 2 leads to - ≈ hc 730 cm-1. Both values for M ) Kr appear to be a factor of two to three higher than normally expected for M ) Kr. However, this difference corresponds well to the general uncertainty of SC SC and of the value of k1,0 reconstructed from the modeling k1,0 measured k1. SC We have compared the two modelings of k1,0 to trace the origin of different results and to emphasize the uncertainties of the modeling. Nevertheless, once is fitted at one temperature, one may relatively well predict the temperature dependence of k1,0 if one relies on the often observed temperature independence of (roughly corresponding to down ∝ T1/2). In the present case, after constructing the falloff curves, one obtains k1,0, which leads to fitted absolute values of and finally leads to predicted expressions of k1,0 over large temperature ranges such as that given below. SC followed the same method as that Our modeling of k3,0 . The employed molecular parameters are again described for kSC 1,0 summarized in the Appendix. For the temperature range 17 2500-4500 K, we derived kSC 3,0 ) [Ar] 1.50 × 10 exp(-53 800 3 -1 -1 K/T) cm mol s . The comparison with the measured k3,0 from eq 7 gives collision efficiencies βc(2900 K) ≈ 0.077 and βc(3800 K) ≈ 0.049. With FE ≈ 1.1, this leads to - ≈ hc SC . This 210 cm-1 with only a weak temperature dependence k3,0 value looks “totally normal” and corresponds well to values derived for related reactions.11,12 3.2. High-Pressure Rate Constants. The present experiments were conducted fairly close to the low pressure limit. Therefore, high-pressure rate constants only need to be known on a semiquantitative level. In ref 2, for the CF3 system, variable reaction coordinate transition state theory was used employing CASPT2/aug-cc-pVDZ calculations of the potential energy surface. This approach led to a nearly temperature-independent value of k-1,∞ ≈ 2.5((0.4) × 1013 cm3 mol-1 s-1 between 300 and 3000 K. Because the employed method is fairly involved, we compared its results with SACM/CT calculations (statistical adiabatic channel model/classical trajectories), as described in ref 17, and their simple empirical representation of the results. After determining the F-CF2 reaction path potential by quantum chemical calculations, as described in ref 18 (on the G3B3 ab initio level), we first obtained the phase space theoretical results PST . Fitting the reaction path potential by a Morse for k-1,∞ ) k-1,∞ expression in this approach led to a Morse parameter β ≈ 3.38 Å-1. The anisotropy of the potential reduces k-1,∞ by a rigidity factor frigid ) k-1,∞/kPST -1,∞. In the treatment of ref 17, the anisotropy is characterized in simplified manner by means of a Pauling parameter, R. Assuming the anisotropy of the potential to be characterized by a standard value of the ratio R/β of 0.5, then,
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Cobos et al. With the SACM/CT approach of ref 17, this then gave frigid ≈ 0.7 to 0.75 for 2500-4000 K and k-3,∞ ≈ 1.8 × 1013 cm3 mol-1 s-1 nearly independent of temperature. 3.3. Falloff Curves. For the present purpose, the construction of the falloff curves of reactions 1 and 3 can be performed with the simplified procedure outlined in refs 11, 19, and 20. Using the measured and/or calculated limiting rate coefficients k0 and k∞ from Sections 3.1 and 3.2 to define the reduced pressure scale x ) k0/k∞, the shape of the reduced falloff curve is approximated by the expression11,19,20 2
1/[1+(log x) ] k0/k∞ ≈ [x/(1 + x)]Fcent
Figure 7. Modeled falloff curves for the dissociation CF2 at T ) 2900 and 3800 K and experimental result (•) from the present work. (See the text.)
Figure 8. Modeled falloff curves for the dissociation CF3 + M f CF2 + F + M at 1625 and 2200 K. Experimental results from the present work (•) with M ) Ar and from ref 2 (7) with M ) Kr. (See the text.)
with the method outlined in ref 17, one derives a nearly temperature-independent value of frigid ≈ 0.5. Finally, one obtains k-1,∞ ≈ 5.9 × 1013 cm3 mol-1 s-1 at 2200 K (with a weak temperature dependence k-1,∞ ∝ T0.2). Because the “standard ratio”, R/β, is a fully empirical guess, one may look into the dependence of k-1,∞ on R/β. For example, for R/β ) 0.4, that is, for a larger anisotropy of the potential, one obtains k-1,∞ ≈ 4.3 × 1013 cm3 mol-1 s-1 at 2200 K. Because the calculations of ref 2 were based not on empirical assumptions about the potential but on true calculations, of course, we prefer k-1,∞ from ref 2. However, we note that the difference between the two calculations of k-1,∞ has no practical importance for the construction of the experimentally relevant part of the falloff curve at 2200 K. (See below.) Because of the smaller number of oscillators in CF2 and the higher temperatures of the experiments, reaction 3 is even closer to the low pressure limit than reaction 1. Therefore, uncertainties of the estimates of k-3,∞ are even less relevant in practice. We have determined k-3,∞ with the same method as that described above for k-1,∞. In this case, however, we had to do quantum chemical calculations ourselves. We employed coupled cluster calculations at the CCSD(T)/6-311+G(3df) level on B3LYP/6-311+G(3df) fully optimized geometries calculated along the minimum energy path. The results were fitted by a potential with an effective Morse parameter of β ) 1.71 Å-1 and an anisotropy ratio R/β ) 0.57.
(11)
with the center broadening factor Fcent. In the present stage, modifications of the broadening factors (by replacing log x by log x/N with N ≈ (0.75 to 1.27) log Fcent) and asymmetries of the falloff curves (see, e.g., refs 19–23) are not introduced. Including strong and weak collision contributions, Fcent is calculated from the properties also determining k0SC, k∞, and βc, as described in ref 11. We first consider the dissociation of CF2, that is, reaction 3. SC WC , and Fcent equal to 0.077, 0.54, and 0.70, With βc, Fcent SC WC Fcent respectively, for T ) 2900 K, one estimates Fcent ) Fcent ≈ 0.38. The corresponding values for T ) 3800 K are 0.049, 0.51, and 0.66, respectively, such that one has Fcent ≈ 0.33. The corresponding falloff curves are constructed with the measured k3,0 from eq 7 and k3,∞ ) 5.3 × 1014 exp(-59 530 K/T) s-1 from the SACM/CT calculations. Figure 7 for T ) 3550 K places the present experimental result on the modeled falloff curve. Clearly, the experimental conditions of the present work correspond well to the limiting low-pressure range. The remaining deviations from low-pressure behavior are well within the experimental scatter, even if the modifications from eq 11 outlined in refs 21–23 were taken into account. The experiments on the dissociation of CF3, that is, reaction 1, from the present work and ref 2 correspond to conditions in the intermediate part of the falloff curve. Employing βc ) 0.29 and 0.12 for M ) Ar and Kr and T ) 1625 and 2200 K, respectively, and using the modeled k0 and k∞ from Sections 3.1 and 3.2, we obtained Fcent ) 0.32 and 0.26, respectively. These values are very close to Fcent ) 0.27 from ref 2, which were obtained by a quite different method. The corresponding falloff curves are shown in Figure 8. The experimental data (converted by the Arrhenius law over small temperature differences to average values of 1625 and 2200 K) fit well to the modeled curves. They are located in the lower part of the falloff curve, being closer to the low-pressure than to the high-pressure limit. Both sets of data are below the limiting low pressure rate coefficients, the data of ref 2 by about a factor of 0.8, and the present data by about a factor of 0.3. One has to expect that eq 11, for the present low values of Fcent, requires some small modifications and that the factors k/k0 are slightly different than given, but again, in the present stage, such changes are within the experimental scatter. 4. Conclusions The present results for the dissociation of CF3 in Ar, assuming that there are no major differences between M ) Ar and Kr, can be combined with the results from ref 2 in Kr in terms of limiting low pressure rate coefficients
k1,0 ) [Kr] 3.5 × 1015 exp(-30 020 K/T) cm3 mol-1 s-1 (12)
Thermal Decomposition of CF3 and CF2 Radicals
J. Phys. Chem. A, Vol. 114, No. 14, 2010 4761
and
k1,∞ ≈ 1.0 × 1015 exp(-41 450 K/T) s-1
(13)
over the range of 1800-2200 K. With Fcent ≈ 0.29 ((0.03) and eq 11, simplified falloff curves over this temperature range can easily be constructed. Asymmetries and additional broadening effects, however, could also be accounted for such as elaborated in ref 19. The present results for the dissociation of CF2 in Ar over the range 2900-3800 K correspond well to the low pressure limit. With the measured
k3,0 ) [Ar] 1.6 × 1015 exp(-48 040 K/T) cm3 mol-1 s-1 (14) and a modeled
k3,∞ ) 5.3 × 1014 exp(-59 530 K/T) s-1
(15)
as well as Fcent ≈ 0.35 ((0.02), eq 11 allows one to construct the complete set of falloff curves for the given temperature range. The present results for reaction 1, together with the results from ref 2 and for reaction 3 supersede the earlier results from refs 1 and 3, which were obtained in shock wave experiments with high reactant concentrations such that nonisothermal conditions were obtained and secondary reactions could not be accounted for properly. Acknowledgment. Technical help from R. Bürsing, K. Oum, and A. Maergoiz is gratefully acknowledged. This work profited from funding within the Max-Planck partner group La Plata Go¨ttingen. A.E.C. also thanks the Alexander von HumboldtFoundation for support. At the 30th International Symposium on Free Radicals at Savonlinna, July 2009, J.T. suggested the use of chemical formulae of free radicals as motifs for composing pieces of music. For example, the F-C-F motif, in transposed form, is used in the Suite Arlesienne No. 2 by Georges Bizet. The formulae of other H-, C-, and F-containing substances could also be used for this purpose, as demonstrated at the Symposium. Appendix Molecular Parameters Used in the Modeling of Rate Coefficients: Vibrational frequencies (in cm-1): CF3: 1253.8 (2), 1086, 701.4, 508.7 (2) from ref 14; CF2: 1225.08, 1114.44, 666.25 from refs 15 and 16. Rotational constants (in cm-1): CF3: A ) B ) 0.364, C ) 0.189, σ ) 3 from refs 24 and 25; CF2: A ) 2.951, B ) 0.420, C ) 0.368, σ ) 2 from ref 26. Enthalpies of formation at 0 K (in kJ mol-1): CF4: -927.23 from ref 27; CF3: -462.75 from ref 13; CF2: -182.42 from ref 27; CF: +251.46 from ref 27; F: +77.28 from ref 27. Lennard-Jones parameters (see ref 28): σ(CF3) ≈ σ(CF4) ) 0.44 nm; ε/k(CF3) ≈ ε/k(CF4) ) 166 K; σ(CF2) ≈ σ(CF3H) ) 0.40 nm, ε/k(CF2) ≈ ε/k(CF3H) ) 268 K; σ(Ar) ) 0.347 nm, σ(Kr) ) 0.366 nm; ε/k(Ar) ) 114 K; ε/k(Kr) ) 178 K. Contributing factors in the modeling of k and Fcent for reactions 1 and 3 are shown in Tables 4 and 5, respectively.
TABLE 4: Contributing Factors in the Modeling of k1,0 and Fcent for Reaction 1: Gvib,h(E0) ≈ 8.2 × 104 (kJ mol-1)-1, Fanh SC ≈ 1.88 (Following ref 29), - ≈ hc 360 cm-1, k1,0 , and WC k1,0 in cm3 mol-1 s-1 T/K
1000
1600
2200
2500
3000
FE Frot kSC 1,0(Ar) βc kWC 1,0 FSC cent Fcent
1.12 7.42 5.25 × 101 0.24 1.26 × 101 0.51 0.42
1.19 5.19 9.47 × 107 0.16 1.52 × 107 0.40 0.31
1.29 3.92 3.87 × 1010 0.12 4.64 × 109 0.36 0.26
1.33 3.47 2.26 × 1011 0.10 2.26 × 1010 0.35 0.25
1.42 2.88 3.69 × 1012 0.086 3.17 × 1011 0.34 0.24
TABLE 5: Contributing Factors in the Modeling of k3,0 and Fcent for Reaction 3: Gvib,h(E0) ≈ 9.0 × 101 (kJ mol-1)-1, Fanh SC ≈ 3.16 (Following ref 29), - ≈ hc 210 cm-1, k3,0 , and WC k3,0 in cm3 mol-1 s-1 T/K
2500
3000
3500
4000
4500
FE Frot kSC 3,0(Ar) βc kWC 3,0 FSC cent Fcent
1.08 18.77 6.46 × 107 0.080 5.17 × 106 0.55 0.38
1.10 14.55 2.58 × 109 0.068 1.75 × 108 0.53 0.36
1.12 11.71 3.34 × 1010 0.059 1.97 × 109 0.52 0.35
1.13 9.44 2.12 × 1011 0.052 1.10 × 1010 0.51 0.34
1.15 8.54 9.34 × 1011 0.046 4.30 × 1010 0.50 0.32
References and Notes (1) Modica, A. P.; Sillers, S. J. J. Chem. Phys. 1968, 48, 3283. (2) Srinivasan, N. K.; Su, M.-C.; Michael, J. V.; Jasper, A. W.; Klippenstein, S. J.; Harding, L. B. J. Phys. Chem. A 2008, 112, 31. (3) Modica, A. P. J. Chem. Phys. 1966, 44, 1585. (4) Skorobogatov, G. A.; Khripun, V. K.; Rebrova, A. G. Kinet. Catal. 2008, 49, 466. (5) Glaenzer, K.; Maier, M.; Troe, J. J. Phys. Chem. 1980, 84, 1681. (6) Croce, A. E.; Cobos, C. J. ; Luther, K. ; Troe, J. J. Phys. Chem. A, submitted. (7) Croce, A. E.; Henning, K.; Luther, K.; Troe, J. Phys. Chem. Chem. Phys. 1999, 1, 5345. (8) Kappel, Ch.; Luther, K.; Troe, J. Phys. Chem. Chem. Phys. 2002, 4, 4329. (9) Croce, A. E., Cobos, C. J.; Luther, K.; Troe, J. J. Phys. Chem. A 2009, DOI: 10.1021/jp9091464. (10) Schug, K. P.; Wagner, H. Gg. Ber. Bunsen-Ges. 1978, 82, 719. (11) Troe, J. J. Phys. Chem. 1979, 83, 114. (12) Troe, J. J. Chem. Phys. 1977, 66, 4745–4758. (13) Ruscic, B.; Michael, J. V.; Redfern, P. C.; Curtiss, L. A. J. Phys. Chem. A 1998, 102, 10889. (14) Forney, D.; Jacox, M. E.; Irikura, K. K. J. Chem. Phys. 1994, 101, 8290. (15) Burkholder, J. B.; Howard, C. J.; Hamilton, P. A. J. Mol. Spectrosc. 1988, 127, 362. (16) Qian, H.-B.; Davies, P. B. J. Mol. Spectrosc. 1995, 169, 201. (17) Maergoiz, A. I.; Nikitin, E. E.; Troe, J.; Ushakov, V. G. J. Chem. Phys. 1998, 108, 5265. (18) Baboul, A. G.; Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. J. Chem. Phys. 1999, 110, 7650. (19) Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 161. (20) Gilbert, R. G.; Luther, K.; Troe, J. Ber. Bunsen-Ges. 1983, 87, 189. (21) Fernandes, R. X.; Luther, K.; Troe, J.; Ushakov, V. G. Phys. Chem. Chem. Phys. 2008, 10, 4313. (22) Troe, J.; Ushakov, V. G. Faraday Discuss. Chem. Soc. 2001, 119, 145. (23) Cobos, C. J.; Troe, J. Z. Phys. Chem. 2003, 217, 1031. (24) Endo, Y.; Yamada, C.; Saito, S.; Hirota, E. J. Chem. Phys. 1982, 77, 3376. (25) Yamada, C.; Hirota, E. J. Chem. Phys. 1983, 78, 1703. (26) Marquez, L.; Demaison, J.; Boggs, J. E. J. Phys. Chem. A 1999, 103, 7632. (27) Chase, M. W., Jr. NIST-JANAF Thermochemical Tables, 4th ed.; Journal of Physical and Chemical Reference Data Monograph 9; American Chemical Society: Washington, D.C., 1998. (28) Hippler, H.; Wendelken, H. J.; Troe, J. J. Chem. Phys. 1983, 78, 6709. (29) Troe, J. Chem. Phys. 1995, 190, 381.
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