Shock wave and modeling study of the reaction CF4 (+M) ⇔ CF3 + F (+M)

Gary Knight a, Lars Sölter b, Elsa Tellbach b and Jürgen Troe *b
aEdwards Innovation Centre, Clevedon, BS21 6TH, UK
bInstitut für Physikalische Chemie, Universität Göttingen, Tammannstrasse 6, D-37077 Göttingen, Germany. E-mail: shoff@gwdg.de

Received 4th May 2016 , Accepted 7th June 2016

First published on 8th June 2016


The thermal decomposition of CF4 (+Ar) → CF3 + F (+Ar) was studied in shock waves over the temperature range 2000–3000 K varying the bath gas concentration [Ar] between 4 × 10−6 and 9 × 10−5 mol cm−3. It is shown that the reaction corresponds to the intermediate range of the falloff curve. By combination with room temperature data for the reverse reaction CF3 + F (+He) → CF4 (+He) and applying unimolecular rate theory, falloff curves over the temperature range 300–6000 K are modeled. A comparison with the reaction system CH4 (+M) ⇔ CH3 + H (+M) is made.


1. Introduction

In spite of its importance in plasma etching and in the pyrolysis and oxidation of fluorocarbons, the dissociation/recombination reaction
 
CF4 (+M) → CF3 + F (+M)(1)
 
CF3 + F (+M) → CF4 (+M)(2)
has only rarely been investigated. There was a single direct shock tube study1 of CF4 dissociation between 2250 and 3100 K in the bath gas M = Ar with [Ar] in the range (0.4–1.9) × 10−5 mol cm−3. Limiting low pressure behavior was postulated with a (pseudo-)first order rate constant of
 
k1 = [Ar] 6.15 × 1034T−4.64[thin space (1/6-em)]exp(−61[thin space (1/6-em)]600 K/T) cm3 mol−1 s−1(3)
The reverse reaction (2) was studied in the bath gas M = He at 295 K as a function of pressure between 0.7 and 7 Torr,2 showing the approach of a pressure independent limiting high pressure second order rate constant of
 
k2,∞ (295 K) = 1.2 × 1013 cm3 mol−1 s−1(4)
This result apparently contradicted results from ref. 3, suggesting an increase of k2 from 0.6 to 3.8 × 1013 cm3 mol−1 s−1 when the pressure of the bath gas Ar varied from 2 to 7 Torr.

Since this earlier work, the equilibrium constant for the dissociation/recombination reaction system

 
Kc = k1/k2 = ([CF3][thin space (1/6-em)][F]/[CF4])eq(5)
has been established more reliably,4–6 such that the data of eqn (3) and (4) can be combined and analyzed in terms of unimolecular rate theory. In doing this, one encounters a number of inconsistencies. In particular, one suspects that reaction (1) in ref. 1 has not been studied in the limiting low pressure range of the unimolecular dissociation but in the intermediate range of the falloff curve. This calls for new experiments over a larger range of bath gas concentrations such as performed in the present work. Furthermore, as the falloff curves are predicted to be “very broad”,7 a combination of experiments with theoretical modeling appears unavoidable. The benefit of this combination of experiments and modeling is the representation of dissociation/recombination rate constants over a wide range of conditions. Because of the uncertain location of the experiments along the falloff curves, however, no new information on the thermodynamics of the system can be derived from the kinetics experiments.

An additional aspect of the present study may be of interest. The comparison of results for the CF4/(CF3 + F)-system with those for the CH4/(CH3 + H)-system should show the effects of replacing the high frequency modes of CH4 by lower frequency modes of CF4. Applying unimolecular rate theory one may inspect whether the differences between the systems can be predominantly be attributed to this effect.

2. Experimental technique and results

We investigated the thermal dissociation of CF4 in the bath gas Ar in incident and in reflected shock waves. Our shock tube had an inner diameter of 9.4 cm, a test section of 4.15 m length, and a high pressure section of 2.80 m length. H2 was used as the driver gas and shock waves were generated by bursting of a diaphragm between the two sections. Further details of our technique were described before8–10 and need not to be repeated here. Mixtures of CF4 (from Linde, 99.9999%) and Ar (from Air Liquide, 99.9999%) were prepared in large mixing vessels before the experiments. Like in ref. 1, the progress of reaction behind the shock waves was followed by recording UV absorption signals of the reaction product CF2. The latter is formed by the dissociation of the primary dissociation product CF3. As the dissociation of CF3 is much more rapid than reaction (1),11 the dissociation of CF4 results in the products CF2 + 2F. In contrast to ref. 1, we worked with highly diluted reaction mixtures. The strong UV absorption of CF2 at 248 nm (decadic absorption coefficient near 2.3 × 106 cm2 mol−1, see ref. 9) allowed us to use mixtures of only 500–1500 ppm of CF4 in Ar. This completely ruled out secondary bimolecular reactions. Our earlier studies of the CF2 spectrum and its wavelength and temperature dependence9 allowed us in addition, to confirm the mass balance of one CF2 formed per one CF4 decomposed (within ±10 percent due to the uncertainty of the absorption coefficient of CF2 and some wall adsorption of CF4 before the experiments, see below). When the mixtures, after decomposition of CF4 behind incident waves, were further heated behind reflected waves, the thermal decomposition of CF2 was also observed, confirming results from ref. 11.

Fig. 1 shows the example of a CF2 absorption-time profile recorded behind a reflected shock. The dissociation is here observed until completion. The final absorption level, with the known absorption coefficient from ref. 9, allows one to control the (minor) extent of CF4 loss by wall adsorption in the mixing vessel. This is of importance for experiments in which the reaction could not be followed to completion during the available measuring time (about 1 ms in reflected waves because of the arrival of dilution waves and about 80 μs in incident waves because of the arrival of the reflected shock).


image file: c6cp03010f-f1.tif
Fig. 1 Absorption-time profile of CF2 at 248 nm in the dissociation CF4 → CF3 + F → CF2 + 2F behind a reflected shock wave (T = 2475 K, [Ar] = 6.9 × 10−5 mol cm−3, relative reactant concentration [CF4]t=0/[Ar] = 5.3 × 10−4).

There is one further observation which needs to be taken into account as a small correction. At temperatures where CF4 does not decompose, one observes small absorption steps behind incident and reflected waves. These can be attributed to the UV absorption continuum of CF4 which broadens with increasing temperature and whose long wavelength tail reaches up to the absorption wavelength 248 nm used for CF2 detection.12 This observation corresponds to decadic absorption coefficients of CF4 at 248 nm of ε = 6.7 × 104 cm2 mol−1 at 980 K and ε = 9.9 × 104 cm2 mol−1 at 1890 K. These values are much smaller than those of CF2 (ε = 2.4 × 106 cm2 mol−1 at 2500 K) such that only small steps at time zero had to be accounted for.

The CF2 absorption-time profiles strictly followed first order time laws

 
[CF2] = [CF4]t=0{1 − exp(−k1t)}(6)

Table 1 presents values of rate constants k1/[Ar] together with the experimental conditions. An Arrhenius representation of the values of k1 is shown in Fig. 2. The data are classified in four groups of Ar concentrations. The high concentration values are apparently systematically lower than the low concentration values. Unfortunately, however, the effect is not large and difficult to characterize quantitatively. Nevertheless, Fig. 2, suggests that the experiments do no correspond to the low pressure limit such as assumed in ref. 1. The modeling presented later on confirms this conclusion. In order to better illustrate the situation, for a temperature of 2500 K Fig. 3 plots the modeled k1 as a function of [Ar]. As the shown experiments were done at temperatures slightly different from 2500 K, the experimental points were converted to 2500 K with an apparent activation energy of 51[thin space (1/6-em)]500 K × R as derived from Fig. 2. In spite of the experimental scatter, the data appear fully consistent with the modeled curve obtained later on. Fig. 2 and 3 also include results from ref. 1. There is good agreement between the two experimental studies when data with the same [Ar] are compared. One should note again, however, that the present results were obtained with much lower CF4 concentrations (0.05–0.15% in the present work vs. 1–2% in ref. 1) and with a much broader variation of [Ar] ((0.4–9) × 10−5 in the present work vs. (0.4–1.9) × 10−5 mol cm−3 in ref. 1). Furthermore, the small additional contribution from CF4 absorption was not recognized in ref. 1 (resulting in a 20% increase of the uncorrected rate constants of ref. 1 for the highest temperatures where in contrast to lower temperatures the CF4 absorption starts to become visible).

Table 1 Experimental conditions (T and [Ar], for relative reactant concentrations of [CF4]t=0/[Ar] = 5 × 10−4) and rate constants k1/[Ar] for the decomposition of CF4
T/K [Ar]/mol cm−3 k 1/[Ar] cm3 mol−1 s−1
2623 5.0 × 10−6 4.8 × 108
2632 5.1 × 10−6 5.0 × 108
2706 4.8 × 10−6 1.4 × 109
2825 4.4 × 10−6 2.3 × 109
2907 4.2 × 10−6 3.8 × 109
3006 4.0 × 10−6 6.4 × 109
2546 1.4 × 10−5 2.5 × 108
2081 5.7 × 10−5 1.5 × 106
2213 5.4 × 10−5 5.1 × 106
2245 5.2 × 10−5 1.1 × 107
2343 4.8 × 10−5 3.5 × 107
2438 4.5 × 10−5 9.3 × 107
2571 4.1 × 10−5 2.7 × 108
2717 3.9 × 10−5 5.2 × 108
2740 5.9 × 10−5 6.0 × 108
2852 3.7 × 10−5 1.6 × 109
2935 3.4 × 10−5 2.7 × 109
2170 9.0 × 10−5 2.1 × 106
2200 8.4 × 10−5 5.1 × 106
2260 8.2 × 10−5 8.5 × 106
2306 7.7 × 10−5 2.8 × 107
2317 8.0 × 10−5 3.4 × 107
2353 7.6 × 10−5 2.1 × 107
2450 7.0 × 10−5 8.0 × 107
2471 7.0 × 10−5 1.2 × 108
2475 6.9 × 10−5 1.0 × 108



image file: c6cp03010f-f2.tif
Fig. 2 Rate constants k1 of the dissociation of CF4 (results from the present work with [Ar] in 10−5 mol cm−3: 6–9: image file: c6cp03010f-u1.tif, 3–6: image file: c6cp03010f-u2.tif, 1–2: image file: c6cp03010f-u3.tif, and 0.4–0.5: image file: c6cp03010f-u4.tif; results from ref. 1: 0.4–0.5: image file: c6cp03010f-u5.tif, and 1–2: image file: c6cp03010f-u6.tif).

image file: c6cp03010f-f3.tif
Fig. 3 Rate constants k1 at T = 2500 K (full line = modeling of this work in comparison to selected experiments from the present work and from ref. 1, see Fig. 2; experimental points converted to 2500 K as described in the text).

3. Modeling of falloff curves

As we expect “broad” falloff curves, i.e. falloff curves with center broadening factors Fc smaller than about 0.4, in the present work we used the representation of reduced falloff curves from ref. 7. The falloff curves are expressed in the form
 
k/k = [x/(1 + x)] F(x)(7)
where k0 and k are the respective limiting low and high pressure first order rate constants, x = k0/k, and F(x) are the broadening factors given by
 
F(x) ≈ (1 + x)/(1 + xn)1/n(8)
with n = [ln[thin space (1/6-em)]2/ln(2/Fc)] (0.8 + 0.2xq) and q = (Fc − 1)[thin space (1/6-em)]ln(Fc/10) (where ln = loge). The crucial quantity here is the center broadening factor Fc which is composed of13,14 a strong collision factor Fscc and a weak collision factor Fwcc. We estimate the former by the method of ref. 15 while the latter requires an estimate of the collision efficiency βc, see ref. 13 (βc later on is derived more precisely from the analysis of k0). Modeling Fscc in ref. 15 by RRKM theory requires activated complex frequencies which, for simplicity, here were taken as those5,6 of CF4 (omitting 909 cm−1 for the reaction coordinate). Modeling Fwcc was done with 〈ΔE〉/hc ≈ −200 cm−1 such as fine-tuned later on. As a first approximation in this way one obtains
 
Fc (M = Ar) ≈ 0.12 + 0.88[thin space (1/6-em)]exp(−T/500 K)(9)
between 1000 and 3000 K, and
 
Fc (M = Ar) ≈ 0.12 + 1.5[thin space (1/6-em)]exp(−18[thin space (1/6-em)]000 K/T)(10)
between 3000 and 6000 K (Fc (M = Ar) ≈ exp(−T/100 K) between 300 and 1000 K). Fc = 0.128 (±0.004) is nearly constant between 2000 and 3000 K. This value indeed corresponds to broad reduced falloff curves such that the representation by eqn (7) and (8) is required. As many of the input parameters of a full master equation treatment are not known well enough, such an approach would not appear warranted at this stage and the simplified method of ref. 7 is sufficient.

When k1,∞ can be estimated, the reduced falloff curves allow for a reconstruction of k1,0, and hence lead to the full absolute falloff curves k1 ([Ar], T). At the present stage, k1,∞ is best estimated with the measurements of k2,∞ near 300 K from ref. 2 and the equilibrium constants Kc. k2,∞ from eqn (4) is of similar order of magnitude as the limiting high pressure rate constant for

 
F + CF2 (+M) → CF3 (+M)(11)
which in ref. 16 was determined to be k11,∞ = 2.5 × 1013 cm3 mol−1 s−1 between 300 and 3000 K. Therefore, it appears safe to assume that k2,∞ is also nearly temperature independent. The comparison with the high pressure rate constant for H + CH3 (+M) → CH4 (+M) is also of interest. According to ref. 17, its value of 2.0 × 1014 (T/300 K)0.15 cm3 mol−1 s−1 also has only a weak temperature dependence. Although these reaction systems are of different character, the resulting conclusions on the temperature coefficient of k2,∞ within experimental uncertainty should be adequate. In the following, k2,∞ = 1.2 × 1013 cm3 mol−1 s−1 from ref. 2 is combined with the equilibrium constant Kc from ref. 5, as represented by
 
Kc = 4.1 × 106T−1[thin space (1/6-em)]exp(−64[thin space (1/6-em)]590 K/T) mol cm−3(12)
between 1000 and 6000 K (we emphasize again that the kinetics results do not contribute much to the given Kc; instead Kc here only can be used to link dissociation and recombination rate constants). This leads to a high pressure dissociation rate constant k1,∞ of
 
k1,∞ ≈ 4.9 × 1019T−1[thin space (1/6-em)]exp(−64[thin space (1/6-em)]590 K/T) s−1(13)
with an estimated uncertainty of about a factor of two. A comparison with the measured rate constants of Table 1 indicates that the present experiments correspond to conditions relatively far from the high pressure range. Combining k1,∞ with modeled reduced falloff curves and comparing the results with the measured k1 then allows one to reconstruct limiting low pressure rate constants. This is done using k1 from Fig. 2 (or a tentatively modeled k1) in order to locate the falloff curves along the pressure axis. Fortunately, the center broadening factors Fc under the present conditions are close to their minimum and practically independent of the conditions. Fitting k1 from Fig. 2, therefore, without problems leads to the true k1,0. Its properties are then further analyzed by unimolecular rate theory in the version of ref. 13. In this analysis there are mainly three contributions which at present stage are difficult to specify, i.e. the centrifugal contributions in the rotational factors Frot, anharmonicity contributions expressed by the anharmonicity factor Fanh, and the average energy transferred per collision 〈ΔE〉 governing the collision efficiency βc. The centrifugal contributions can be handled with the C–F potential in CF3, see ref. 11, and were found to be relatively unimportant. That leaves the product 〈ΔEFanh to be fitted with the experimental k1,0. As this product is expected not to depend strongly on the temperature, one cannot separate it by analysis of falloff curves at different temperatures. However, fitting 〈ΔEFanh at one temperature and using this value in the theoretically modeled k1,0, one can control the result by analyzing falloff curves at different temperatures, here with the experiments near 2000 and 3000 K. Because of the marked shift of the falloff curves along the pressure scale, this is particularly meaningful in the present case. The results are of similar quality as Fig. 3 for 2500 K. We note that we fit a value of the product 〈ΔEFanh/hc of about −560 cm−1. Assuming 〈ΔE〉/hc ≈ −200 cm−1, this corresponds to Fanh ≈ 2.8. Both values appear to be slightly high, but they may include uncertainties from other contributing factors. In any case, the corresponding modeled k1,0 can reliably be used for extrapolations to other temperatures. Between 2000 and 6000 K (within a factor of about two) it can be represented in the form
 
k1,0 ≈ [Ar] 1.5 × 1051T−9[thin space (1/6-em)]exp(−64[thin space (1/6-em)]590 K/T) cm3 mol−1 s−1(14)
which after conversion with Kc from eqn (12) corresponds to
 
k2,0 ≈ [Ar] 3.7 × 1044T−8 cm6 mol−2 s−1(15)
between 2000 and 3000 K (and k2,0 ≈ [Ar] 4.7 × 1033T−4.7 cm6 mol−2 s−1 between 300 and 2000 K). The marked shift of the falloff curves along the [Ar]-axis most easily is illustrated by plotting k2vs. [Ar] at different temperatures. This is done in Fig. 4. The experimental results from the present work, after conversion by eqn (12), and the results from ref. 2 for 295 K (after accounting for the change of the bath gas to He, with 〈ΔE〉/hc ≈ −20 cm−1) are well represented by these falloff curves. The modeled falloff curve for T = 2500 K in Fig. 3 shows that, because of the experimental scatter, the deviations of the measured k1 from k1,0 could not have been quantified without the modeling.


image file: c6cp03010f-f4.tif
Fig. 4 Modeled falloff curves for k2, i.e. for the recombination F + CF3 (+Ar) → CF4 (+Ar) (from left to right for T = 300, 1000, 2000, and 3000 K).

Comparing falloff curves for the recombination of the CH4- and CF4-systems in Fig. 5, one realizes that, at a given temperature, the CF4-system is closer to the high pressure limit than the CH4-system. This is attributed to the larger vibrational density of states at the dissociation threshold in CF4 which arises from the lower fundamental frequencies and the larger dissociation energy and which leads to a larger k1,0. The effect in part is compensated by the smaller Fc-values in the CF4-system and, thus, the broader falloff curves. In addition, however, the larger high pressure recombination rate constant for CH4 also influences the position of the falloff curves.


image file: c6cp03010f-f5.tif
Fig. 5 Comparison of modeled falloff curves for k2 from this work for F + CF3 (+Ar) → CF4 (+Ar) (lower set of curves: data from Fig. 4) and for H + CH3 (+Ar) → CH4 (+Ar) (upper pair of curves: data from ref. 17, for T = 300 and 3000 K from left to right).

4. Conclusions

The present CF4 dissociation experiments in combination with low temperature recombination data allowed us to provide an internally consistent set of rate constants k1([Ar],T) and k2([Ar],T). As the falloff curves of the two reactions were shown to be broad, only the combination of experiments and unimolecular rate theory was able to provide the full picture. The Appendix summarizes the derived rate parameters allowing for a representation of the relevant rate constants over the range 300–6000 K.

Appendix: modeled rate parameters

Temperature range 300–2000 K: k2,0 ≈ [Ar] 4.7 × 1033T−4.7 cm6 mol−2 s−1 and k2,∞ ≈ 1.2 × 1013 cm3 mol−1 s−1.

Temperature range 2000–6000 K: k1,0 ≈ [Ar] 1.5 × 1051T−9[thin space (1/6-em)]exp(−64[thin space (1/6-em)]590 K/T) cm3 mol−1 s−1, k1,∞ ≈ 4.9 × 1019T−1[thin space (1/6-em)]exp(−64[thin space (1/6-em)]590 K/T) s−1, and Kc = 4.1 × 106T−1[thin space (1/6-em)]exp(−64[thin space (1/6-em)]590 K/T) mol cm−3.

Center broadening factors: Fc (M = Ar) = 0.71, 0.22, 0.13, 0.12, 0.14, and 0.20 for T/K = 300, 1000, 2000, 3000, 4000, and 6000; these results can be represented by Fc (M = Ar) = exp(−T/100 K) between 300 and 1000 K, 0.12 + 0.88[thin space (1/6-em)]exp(−T/500 K) between 1000 and 3000 K, and 0.12 + 1.5[thin space (1/6-em)]exp(−18[thin space (1/6-em)]000 K/T) between 3000 and 6000 K.

Broadening factors: it was shown in ref. 7 and 14 that broadening factors F(x) for different reaction systems can be represented in terms of a single parameter Fc only within certain limits, deviating up to about ±10% from eqn (8). However, because of the present small values of Fc, the simpler “standard form” of F(x) from ref. 13 cannot be used here. A comparison of eqn (8) with the large number of alternative propositions cited in ref. 7 remains to be done with respect to their suitability (simplicity and realistic results).

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