Gary
Knight
^{a},
Lars
Sölter
^{b},
Elsa
Tellbach
^{b} and
Jürgen
Troe
*^{b}
^{a}Edwards Innovation Centre, Clevedon, BS21 6TH, UK
^{b}Institut 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 CF_{4} (+Ar) → CF_{3} + 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 CF_{3} + F (+He) → CF_{4} (+He) and applying unimolecular rate theory, falloff curves over the temperature range 300–6000 K are modeled. A comparison with the reaction system CH_{4} (+M) ⇔ CH_{3} + H (+M) is made.

CF_{4} (+M) → CF_{3} + F (+M) | (1) |

CF_{3} + F (+M) → CF_{4} (+M) | (2) |

k_{1} = [Ar] 6.15 × 10^{34}T^{−4.64}exp(−61600 K/T) cm^{3} mol^{−1} s^{−1} | (3) |

k_{2,∞} (295 K) = 1.2 × 10^{13} cm^{3} mol^{−1} s^{−1} | (4) |

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

K_{c} = k_{1}/k_{2} = ([CF_{3}][F]/[CF_{4}])_{eq} | (5) |

An additional aspect of the present study may be of interest. The comparison of results for the CF_{4}/(CF_{3} + F)-system with those for the CH_{4}/(CH_{3} + H)-system should show the effects of replacing the high frequency modes of CH_{4} by lower frequency modes of CF_{4}. Applying unimolecular rate theory one may inspect whether the differences between the systems can be predominantly be attributed to this effect.

Fig. 1 shows the example of a CF_{2} 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 CF_{4} 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).

There is one further observation which needs to be taken into account as a small correction. At temperatures where CF_{4} does not decompose, one observes small absorption steps behind incident and reflected waves. These can be attributed to the UV absorption continuum of CF_{4} which broadens with increasing temperature and whose long wavelength tail reaches up to the absorption wavelength 248 nm used for CF_{2} detection.^{12} This observation corresponds to decadic absorption coefficients of CF_{4} at 248 nm of ε = 6.7 × 10^{4} cm^{2} mol^{−1} at 980 K and ε = 9.9 × 10^{4} cm^{2} mol^{−1} at 1890 K. These values are much smaller than those of CF_{2} (ε = 2.4 × 10^{6} cm^{2} mol^{−1} at 2500 K) such that only small steps at time zero had to be accounted for.

The CF_{2} absorption-time profiles strictly followed first order time laws

[CF_{2}] = [CF_{4}]_{t=0}{1 − exp(−k_{1}t)} | (6) |

Table 1 presents values of rate constants k_{1}/[Ar] together with the experimental conditions. An Arrhenius representation of the values of k_{1} 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 k_{1} 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 51500 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 CF_{4} 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 CF_{4} 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 CF_{4} absorption starts to become visible).

T/K | [Ar]/mol cm^{−3} |
k
_{1}/[Ar] cm^{3} mol^{−1} s^{−1} |
---|---|---|

2623 | 5.0 × 10^{−6} |
4.8 × 10^{8} |

2632 | 5.1 × 10^{−6} |
5.0 × 10^{8} |

2706 | 4.8 × 10^{−6} |
1.4 × 10^{9} |

2825 | 4.4 × 10^{−6} |
2.3 × 10^{9} |

2907 | 4.2 × 10^{−6} |
3.8 × 10^{9} |

3006 | 4.0 × 10^{−6} |
6.4 × 10^{9} |

2546 | 1.4 × 10^{−5} |
2.5 × 10^{8} |

2081 | 5.7 × 10^{−5} |
1.5 × 10^{6} |

2213 | 5.4 × 10^{−5} |
5.1 × 10^{6} |

2245 | 5.2 × 10^{−5} |
1.1 × 10^{7} |

2343 | 4.8 × 10^{−5} |
3.5 × 10^{7} |

2438 | 4.5 × 10^{−5} |
9.3 × 10^{7} |

2571 | 4.1 × 10^{−5} |
2.7 × 10^{8} |

2717 | 3.9 × 10^{−5} |
5.2 × 10^{8} |

2740 | 5.9 × 10^{−5} |
6.0 × 10^{8} |

2852 | 3.7 × 10^{−5} |
1.6 × 10^{9} |

2935 | 3.4 × 10^{−5} |
2.7 × 10^{9} |

2170 | 9.0 × 10^{−5} |
2.1 × 10^{6} |

2200 | 8.4 × 10^{−5} |
5.1 × 10^{6} |

2260 | 8.2 × 10^{−5} |
8.5 × 10^{6} |

2306 | 7.7 × 10^{−5} |
2.8 × 10^{7} |

2317 | 8.0 × 10^{−5} |
3.4 × 10^{7} |

2353 | 7.6 × 10^{−5} |
2.1 × 10^{7} |

2450 | 7.0 × 10^{−5} |
8.0 × 10^{7} |

2471 | 7.0 × 10^{−5} |
1.2 × 10^{8} |

2475 | 6.9 × 10^{−5} |
1.0 × 10^{8} |

Fig. 2 Rate constants k_{1} of the dissociation of CF_{4} (results from the present work with [Ar] in 10^{−5} mol cm^{−3}: 6–9: , 3–6: , 1–2: , and 0.4–0.5: ; results from ref. 1: 0.4–0.5: , and 1–2: ). |

Fig. 3 Rate constants k_{1} 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). |

k/k_{∞} = [x/(1 + x)] F(x) | (7) |

F(x) ≈ (1 + x)/(1 + x^{n})^{1/n} | (8) |

F_{c} (M = Ar) ≈ 0.12 + 0.88exp(−T/500 K) | (9) |

F_{c} (M = Ar) ≈ 0.12 + 1.5exp(−18000 K/T) | (10) |

When k_{1,∞} can be estimated, the reduced falloff curves allow for a reconstruction of k_{1,0}, and hence lead to the full absolute falloff curves k_{1} ([Ar], T). At the present stage, k_{1,∞} is best estimated with the measurements of k_{2,∞} near 300 K from ref. 2 and the equilibrium constants K_{c}. k_{2,∞} from eqn (4) is of similar order of magnitude as the limiting high pressure rate constant for

F + CF_{2} (+M) → CF_{3} (+M) | (11) |

K_{c} = 4.1 × 10^{6}T^{−1}exp(−64590 K/T) mol cm^{−3} | (12) |

k_{1,∞} ≈ 4.9 × 10^{19}T^{−1}exp(−64590 K/T) s^{−1} | (13) |

k_{1,0} ≈ [Ar] 1.5 × 10^{51}T^{−9}exp(−64590 K/T) cm^{3} mol^{−1} s^{−1} | (14) |

k_{2,0} ≈ [Ar] 3.7 × 10^{44}T^{−8} cm^{6} mol^{−2} s^{−1} | (15) |

Fig. 4 Modeled falloff curves for k_{2}, i.e. for the recombination F + CF_{3} (+Ar) → CF_{4} (+Ar) (from left to right for T = 300, 1000, 2000, and 3000 K). |

Comparing falloff curves for the recombination of the CH_{4}- and CF_{4}-systems in Fig. 5, one realizes that, at a given temperature, the CF_{4}-system is closer to the high pressure limit than the CH_{4}-system. This is attributed to the larger vibrational density of states at the dissociation threshold in CF_{4} which arises from the lower fundamental frequencies and the larger dissociation energy and which leads to a larger k_{1,0}. The effect in part is compensated by the smaller F_{c}-values in the CF_{4}-system and, thus, the broader falloff curves. In addition, however, the larger high pressure recombination rate constant for CH_{4} also influences the position of the falloff curves.

Fig. 5 Comparison of modeled falloff curves for k_{2} from this work for F + CF_{3} (+Ar) → CF_{4} (+Ar) (lower set of curves: data from Fig. 4) and for H + CH_{3} (+Ar) → CH_{4} (+Ar) (upper pair of curves: data from ref. 17, for T = 300 and 3000 K from left to right). |

Temperature range 2000–6000 K: k_{1,0} ≈ [Ar] 1.5 × 10^{51}T^{−9}exp(−64590 K/T) cm^{3} mol^{−1} s^{−1}, k_{1,∞} ≈ 4.9 × 10^{19}T^{−1}exp(−64590 K/T) s^{−1}, and K_{c} = 4.1 × 10^{6}T^{−1}exp(−64590 K/T) mol cm^{−3}.

Center broadening factors: F_{c} (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 F_{c} (M = Ar) = exp(−T/100 K) between 300 and 1000 K, 0.12 + 0.88exp(−T/500 K) between 1000 and 3000 K, and 0.12 + 1.5exp(−18000 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 F_{c} only within certain limits, deviating up to about ±10% from eqn (8). However, because of the present small values of F_{c}, 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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