Falloff curves and mechanism of thermal decomposition of CF₃I in shock waves

Abstract

The falloff curves of the unimolecular dissociation CF₃I (+Ar) → CF₃ + I (+Ar) are modelled by combining quantum-chemical characterizations of the potential energy surface for the reaction, standard unimolecular rate theory, and experimental information on the average energy transferred per collision between excited CF₃I and Ar. The (essentially) parameter-free theoretical modelling gives results in satisfactory agreement with data deduced from earlier shock wave experiments employing a variety of reactant concentrations (between a few ppm and a few percent in the bath gas Ar). New experiments recording absorption–time signals of CF₃I, I₂, CF₂ and (possibly) IF at 450–500 and 200–300 nm are reported. By analysing the decomposition mechanism, besides the unimolecular dissociation of CF₃I, these provide insight into the influence of secondary reactions on the experimental observations.

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I. Introduction

The thermal decomposition of CF₃I has attracted considerable interest for a number of reasons. On the one hand, it has served as a source of CF₃ radicals in shock waves.^1–3 On the other hand, with its weak C–I bond in the presence of strong C–F bonds, it represents a prototype of a unimolecular dissociation reaction of simple bond-fission character.^4–15 Furthermore, its secondary reactions are related to processes of importance in chemical lasers and laser-induced isotope separation.^16,17 The role of secondary reactions, in flow system studies of CF₃I dissociation up to about 800 K, remained unclear for quite some while. Only shock wave experiments, using iodine atom resonance absorption spectroscopy (ARAS) and employing very low reactant CF₃I concentrations,^13,15 directly led to the rate constant of the unimolecular reaction. Although some modelling of this rate constant in its falloff range had been made in earlier work, only with the ARAS results such modelling could be put on a safe basis.¹⁵ Nevertheless, the theoretical approach to the falloff curves left something to be desired. First, it was based on only simplified versions of Rice–Ramsperger–Kassel–Marcus (RRKM) theory. This approach in the present work is extended by accounting for the finer details of the potential energy surface along the reaction coordinate. Second and more seriously, the average energy 〈ΔE〉 transferred per collision between the bath gas M and excited CF₃I (or the equivalent collision efficiency β_c) was only treated as a fit parameter. It was overlooked that 〈ΔE〉 (for the bath gas M = Ar) had been measured directly in IR-multiphoton excitation experiments.^18–21 With the background of the mentioned experimental and theoretical studies, it appeared attractive to us to investigate the reaction again and in greater detail. We model the rate constant in terms of loose-activated complex unimolecular rate theory, determining the required molecular parameters by quantum-chemical calculations. After introducing the experimental 〈ΔE〉, falloff curves are constructed and expressed in the form recommended in ref. 22 and 23. The influence of uncertainties in the C–I bond energy is also investigated. Finally, a comparison with the ARAS shock wave results is made.

Having established reliable falloff curves, new shock wave experiments were performed using alternatives to the ARAS detection method. While the ARAS experiments used reactant concentrations as low as 1–4 ppm of CF₃I in Ar¹⁵ (or in Kr¹³), the present work employs mixtures with 100–1500 ppm (mostly about 500 ppm). The present experiments were able to monitor CF₃I concentrations with considerably reduced reactant concentrations in comparison to earlier shock tube work (employing reactant concentrations of 0.5–5%^6,9,14). Within the present range of reactant concentrations, the onset of secondary reactions can be monitored. Insight into the complex thermal decomposition mechanism is obtained with the help of absorption spectroscopy in the ranges 200–300 and 450–500 nm. On the basis of the detailed reaction mechanism (being probably still incomplete), the previous high-concentration shock wave experiments could also be reinterpreted. Finally, the identification of species with so far unknown high-temperature absorption coefficients was facilitated by quantum-chemical calculations of oscillator strengths.

II. Modelling of dissociation rate constants

Our modelling of rate constants for the unimolecular dissociation of the C–I bond in CF₃I, first, focussed on the properties of the minimum-energy path (MEP) potential V(r) of the reaction and the change of transitional mode quanta ν(r) along the MEP reaction coordinate r. V(r) and ν(r) were derived by quantum-chemical calculations. A 6-311G(d) basis set for I atoms as tabulated in ref. 24 and 25 and a 6-311+G(3df) basis set for C and F atoms were employed. With these basis sets optimized structures and vibrational frequencies were calculated at the M06-2X level (for details of our approach, see e.g.ref. 26–30; more details are given in the ESI†). V(r) (computed at the CCSD(T)//M06-2X level) could be approximated using a Morse function (with the Morse parameters β ≈ 1.45 Å⁻¹, r_e ≈ 2.16 Å, and D_e = 225.9 kJ mol⁻¹). The transitional mode quanta ν(r) were found to decay exponentially along the MEP (with decay parameters α ≈ 0.59 and 0.61 Å⁻¹, such that the ratio α/β is not far from the “standard value” α/β ≈ 0.5³¹). The calculation of the rotational contributions requires the determination of centrifugal maxima along the MEP. This was done with the r-dependence of the rotational constant of CF₃I (being approximated using (B + C)/2 ≈ 0.0505 cm⁻¹/[1 + 0.551(r − 2.16 Å) + 0.138(r − 2.16 Å)²]). Graphical representations of V(r), ν(r), and (B + C)/2 for the CF₃–I bond are given in Fig. S1–S3 of the ESI.†

The pseudo-first order rate constant k₁ of the unimolecular dissociation CF₃I → CF₃ + I is expressed in its usual form k₁/k_1,∞ = [x/(1 + x)]F(x), with x = k_1,0/k_1,∞ (the limiting low-pressure rate constant k_1,0 being proportional to the bath gas concentration [M] = Ar, while the limiting high-pressure rate constant k_1,∞ is independent of [M]; F(x) denotes a suitable “broadening factor”, see below).

With the information obtained and using the statistical adiabatic channel model (in its classical trajectory version, SACM/CT, from ref. 32), limiting high-pressure rate constants

k_1,∞ = 5.9 × 10¹⁵(T/1000 K)^−2.2exp(−28 930 K/T) s⁻¹ (1)

were derived (for a value of the reaction enthalpy at 0 K of ³³). Using 〈ΔE〉/hc ≈ −100 cm⁻¹ independent of temperature, such as that determined experimentally for M = Ar in ref. 21, and employing the formalism of ref. 34, limiting low-pressure rate constants

k_1,0 = [Ar]5.4 × 10²¹(T/1000 K)^−10.5exp(−31 360 K/T)cm³ mol⁻¹ s⁻¹ (2)

were calculated (the given value of 〈ΔE〉 between 750 and 2000 K corresponds to the collision efficiency β_c ≈ 0.076(1000 K/T)^1.2, see the ESI†). The construction of falloff curves following ref. 22 and 23, furthermore, requires information on center broadening factors of the falloff curves F_cent = F(x = 1).³⁴ These were derived with the method proposed in ref. 23 and 35 (leading to F_cent = 0.20, 0.16, 0.14, and 0.14 at T/K = 750, 1000, 1500, and 2000, respectively). Fig. 1 shows the corresponding falloff curves for selected temperatures. The latter were chosen to be 950, 1050, and 1200 K, in order to compare with the modelling from ref. 15 (which used variational RRKM theory for k_1,∞, while k_1,0 was derived following ref. 34 with an assumed β_c ≈ 100 K/T and F_cent = 0.188). Fig. 1 shows that the limiting values of the present falloff curves differ considerably from those of ref. 15. The figure also includes experimental ARAS results from ref. 15 (the measured points were corrected for slight temperature “mismatch” using the modelled temperature dependence of the rate constants at the given [Ar]). The agreement between the ARAS data and the modelled falloff curves appears quite satisfactory. While the differences in the modelled k_1,∞ are only small, larger discrepancies are observed in the modelled limiting low-pressure rate constants k_1,0. This could be due to differences in several input factors (see the basic formalism from ref. 34). The most probable reason seems to us to be that centrifugal barriers were accounted for in the present work (on the basis of Fig. S3 of the ESI†), while this was not done or done differently in ref. 15. This reduces the rotational factors F_rot in k_1,0. A further analysis of the difference does not appear warranted at this stage.

Fig. 1 Falloff curves for the unimolecular dissociation CF₃I → CF₃ + I (full lines: modelling from this work (see Section III), dashed lines: modelling from ref. 15; experimental results from this work: ● (1200 K), ■ (1050 K); from ref. 15: ○ (1200 K), □ (1050 K), Δ (950 K); from ref. 8: × (1200 K, reevaluated); influence of secondary reactions in the present work and in ref. 8 accounted for: see Section III).

We also inspected the influence of uncertainties in the reaction enthalpy. Increasing by 4 kJ mol⁻¹ decreases k₁ (at [Ar] = (5 × 10⁻⁵–1.5 × 10⁻⁴) mol cm⁻³) by a factor of 1.5–2 (decreasing by 4 kJ mol⁻¹ increases k₁ by the same factor). Measurements and modelled (unadjusted) falloff curves, therefore, agree better than this uncertainty and confirm the validity of the thermochemistry used in the literature.^33,36,37 Nevertheless, the finer details of the shape of the falloff curves should also be noted. In particular, different approaches of k₁ toward the limiting low- and high-pressure rate constants (k_1,0 and k_1,∞, resp.) are to be accounted for when the more recent falloff expressions from ref. 22 and 23 are used instead of the older forms from ref. 34. The modelling of the falloff curves and their comparison with the ARAS results from ref. 15 in the foregoing section has been described in detail, because it forms the basis for an analysis of the decomposition mechanism under conditions of higher reactant concentrations. This analysis will be made after new experiments are described in the following section.

III. Experimental CF₃I absorption signals

Experiments in the present work were performed in incident and in reflected shock waves in the bath gas Ar. The progress of reaction was followed by recording absorption–time profiles at selected wavelengths in the ranges 200–300 nm and 450–500 nm. Details of our experimental technique have been described before and need not be repeated here (see, e.g., ref. 27–30 and 38–40). Our experiments used reaction mixtures prepared in large mixing vessels before being introduced into a shock tube. Mixtures of CF₃I (99% purity, from Sigma-Aldrich) and Ar (99.9999% purity, from Air Liquide) with reactant concentrations between about 100 and 1500 ppm of CF₃I in Ar (mostly about 500 ppm) were employed. The chosen concentrations are of importance for the analysis of the dissociation mechanism, see below.

In the first part of our experiments we followed the progress of reaction by monitoring the concentration of the decomposing CF₃I, recording absorption signals near the absorption maximum at 271 nm.⁶ Two examples of the recorded absorption–time profiles are shown in Fig. 2 and 3. The absorption increases abruptly at the arrival of the incident shock, marked by the first Schlieren peak. The second Schlieren peak indicates the arrival of the reflected shock. The second absorption rise then is followed by the decay of the CF₃I absorption due to reaction. The evaluation of the signals requires careful reconstruction of the room temperature absorption level before the arrival of the incident shock. One also has to reconstruct the absorption level directly behind the reflected shock in order to separate the absorption step and Schlieren peak. These operations could be done with the help of the temperature-dependent absorption coefficients of CF₃I determined in ref. 6 and 41. Finally, the zero-absorption line also had to be reconstructed. A temperature of 622 K behind the incident shock in Fig. 2 is too low to produce substantial dissociation of CF₃I before the arrival of the reflected shock. At a temperature of 1030 K behind the reflected shock, however, the dissociation of CF₃I sets in. It is important to note that the dissociation is not complete within the observation time of about 1.3 ms. This is of relevance when the reaction mechanism is considered in more detail, see below. It is also important to note that the disappearance of CF₃I in Fig. 2 and 3 considerably slows with increasing reaction time and does not reach the zero-absorption line.

Fig. 2 Absorption–time profile of decomposing CF₃I, recorded at 271 nm (532 ppm of CF₃I in Ar, T = 1031 K, [Ar] = 1.56 × 10⁻⁴ mol cm⁻³).

Fig. 3 As Fig. 2, but at higher temperatures (536 ppm of CF₃I in Ar, T = 1219 K, [Ar] = 1.27 × 10⁻⁴ mol cm⁻³).

The initial rate of CF₃I disappearance was represented by a first-order rate law,

[CF₃I] ≈ [CF₃I]_t=0exp(−kt) (3)

with an apparent rate constant k. Experimental values of k were derived from reflected shocks (for [Ar] larger than 10⁻⁴ mol cm⁻³) and from incident shocks (for [Ar] in the range of (2–4) × 10⁻⁵ mol cm⁻³). In spite of the similarity of the recorded signals shown in Fig. 2 and 3 to the signal reported in ref. 8 (for 20 times larger [CF₃I]_t=0), it is by no means clear that the apparent initial rate constant k corresponds to the rate constant k₁ for the unimolecular dissociation of CF₃I. This interpretation requires further analysis of the decomposition mechanism given below.

The thermal decomposition of CF₃I traditionally has been discussed in terms of the reactions summarized in Table 1. For the high-temperature conditions of the present work, a number of aspects are important to note. First, the reverse reactions of all reactions have to be included (this was done here with equilibrium constants from the tabulations in ref. 33). Second, information on the two primary secondary reactions of I (reaction (R2)) and CF₃ (reaction (R4)) with CF₃I is needed. As this is available only for low temperatures,^12,42–44 the corresponding rate constants k₂ and k₄ here were treated as uncertain parameters and their influence was investigated. k₃ was taken unchanged from ref. 45 and k₅ from ref. 39. Simulating the kinetics of the reactions given in Table 1 leads to concentration–time profiles of CF₃I such as those shown in Fig. 4. The plot of [CF₃I]/[CF₃I]_t=0 as a function of k₁t well reproduces the experimentally observed slowing of the CF₃I decomposition rate with time t. It is essential not to increase the fitted rate constant k₁ beyond the given value because this would strongly reduce the overall yield of the reaction (a decrease of k₋₁ on the other hand would have no influence). An increase of k₂ by a factor of 10 reduces the calculated half-life of CF₃I by only 4% while an increase of k₄ by a factor of 10 has an even smaller effect. The concentration–time profiles of CF₃I thus are unsuitable for fitting k₂ and k₄. Extracting k₁ from the CF₃I profiles, however, required accounting for the slowing of the decomposition. As the [CF₃I]/[CF₃I]_t=0 profile as a function of k₁t hardly varies with temperature (see Fig. 4), the profile shown in Fig. 4 could be used for extracting k₁ from the initial rate constant k of eqn (3) or, better, from a fit of the complete measured CF₃I profile to the kinetics simulation. The resulting k₁ values are summarized in Table 2. Selected values are included in Fig. 1 and compared with the ARAS data from ref. 15 and the modelled falloff curves. All data are consistent with each other. Increasing the reactant concentration from the 532 ppm of Fig. 2 and 3 to the 2% in ref. 8 has a noticeable effect: it increases the CF₃I half-life by a factor of 1.6. The correspondingly reevaluated value is included in Fig. 1; it agrees well with the other results shown (the agreement with the data from ref. 6 is less satisfactory, because full CF₃I profiles were not reported in ref. 6).

Table 1 Mechanism of the thermal decomposition of CF₃I (notes: (a) k₁ = 4.0 × 10¹²exp(−22 790 K/T) s⁻¹ modelled with for [Ar] ≈ 1.5× 10⁻⁴ mol cm⁻³ over the range 1000–1050 K; (b) reverse reaction: equilibrium constant from ref. 33; (c) k₂ = 7.6 × 10¹²exp(−9500 K/T) cm³ mol⁻¹ s⁻¹ for 400–900 K, from ref. 42–44; (d) k₃ = [Ar]8.8 × 10¹³exp(−14 950 K/T) s⁻¹ for 1080–1570 K and [Ar] = (0.3–1) × 10⁻⁶ mol cm⁻³, from ref. 45 and 46; (e) k₄ ≤ 1.2 × 10⁸ cm³ mol⁻¹ s⁻¹ for 300 K, from ref. 16; (f) k₋₅ ≤ 1.2 × 10¹³ cm³ mol⁻¹ s⁻¹ for 1200 K and [Ar] = 10⁻⁴ mol cm⁻³ from ref. 47–49)

Number	Reaction	Notes
R1	CF3I → CF3 + I	a, b
R2	I + CF3I → I2 + CF3	c, b
R3	I2 + Ar → 2I + Ar	d, b
R4	CF3 + CF3I → C2F6 + I	e, b
R5	CF3 + CF3 → C2F6	f, b

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Fig. 4 Kinetics simulation of CF₃I concentration–time profiles (c = [CF₃I], c₀ = [CF₃I]_t=0, full lines: simulation with reactions of Table 1 for 500 ppm of CF₃I in Ar, dashed line: for 2% of CF₃I in Ar; *: profile without secondary reactions, k₁ = rate constant for unimolecular dissociation of CF₃I, t = time, see Section III).

Table 2 Experimental rate constants k₁ for the unimolecular dissociation CF₃I → CF₃ + I (present work, evaluated with the reaction mechanism of Section III)

T/K	[Ar]/mol cm^−3	k 1/s^−1
1005	3.2 × 10^−5	5.5 × 10^2
1031	1.6 × 10^−4	6.0 × 10^2
1045	6.5 × 10^−5	1.3 × 10^3
1076	5.8 × 10^−5	4.5 × 10^3
1130	5.7 × 10^−5	6.5 × 10^3
1152	2.5 × 10^−5	5.6 × 10^3
1160	1.4 × 10^−4	1.3 × 10^4
1195	9.0 × 10^−5	7.8 × 10^3
1219	1.3 × 10^−4	2.5 × 10^4
1220	1.3 × 10^−4	2.0 × 10^4

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Although the measured CF₃I absorption–time profiles of the present work appear consistent with the modelling of k₁, additional measurements of I₂ signals as described in the following section raise questions, suggesting that further reactions need to be considered. At this moment it appears uncertain whether they have an influence on kinetics simulations of CF₃I profiles such as those shown in Fig. 4. Because the agreement of experimental and modelled k₁ values in Fig. 1 looks satisfactory, one is tempted to assume that this is not the case.

IV. Experimental I₂ absorption signals

The simulation of the CF₃I profiles described in Section III indicated that conclusions on the rate constants k₂ and k₄ of reactions (R2) and (R4) could be drawn only to a limited extent, while the CF₃I profiles independent of uncertainties in the mechanism led to k₁. In order to learn more about k₂ and k₄, profiles of intermediate reaction species should be measured. Information on CF₃-profiles would be difficult to obtain, because the absorption coefficient of this intermediate in the investigated spectral range (at wavelengths larger than 200 nm) is only a small value.⁵⁰ We have, furthermore, extended the measurements of absorption coefficients of CF₂ to wavelengths near 200 nm (CF₂ prepared by the thermal decomposition CHF₃ → CF₂ + HF,³⁸ see also ref. 27 and 51). We found that CF₂ (from reactions not included in Table 1) or the strong absorber CF (which forms at considerably higher temperatures in the thermal decomposition of CF₂⁴⁰) would not contribute to absorption signals of the present work. In contrast to this, I₂ should be detectable, either in the intense Cordes bands near 200 nm or in the visible range 450–500 nm. Fig. 5 and 6 show examples for 200 and 487 nm under similar experimental conditions. While the I₂ absorption coefficients at 487 nm are observed under shock wave conditions,^45,46 they are observed near 200 nm only at near room temperature.^51–54Fig. 5 and 6 show the absorption signals from I₂, one then could calibrate the high temperature absorption coefficients of I₂ near 200 nm against those from 450 to 500 nm. However, this procedure faces the following problem. Fig. 7 shows an absorption signal at 487 nm for conditions close to those of Fig. 2. The kinetics simulation predicts a profile such as that included in Fig. 7. This considerably differs from the observations. Furthermore, absorption signals at the wavelengths of Fig. 5–7 were still observable at temperatures in the range of 1300–1600 K where I₂ should have disappeared by thermal decomposition (at even higher temperatures these signals finally disappeared). Apparently besides I₂ an additional species must have contributed to the signals shown in Fig. 5–7 and it has similar spectral properties to I₂, but is thermally more stable. Quantum-chemical calculations of oscillator strengths (for IF, I₂, CF, CFI, CF₂I, CF₃I, and CF₂, see the ESI†) indicated that this can only be IF. This species is thermally more stable than I₂ (dissociation enthalpy for IF instead of 148.8 kJ mol⁻¹ for I₂³³). Its calculated oscillator strength is even larger than that of I₂ in the range of the visible spectrum (see the ESI†). Unfortunately, so far only information from the emission spectra of IF at 450–650 nm is available (see, e.g.ref. 55 and 56), but this looks consistent with the present identification of the additional species. IF might be formed in the reaction

I + CF₃ → IF + CF₂ (R6)

followed by reactions consuming CF₂ and the dissociation of IF. An alternative could be a second, high energy, dissociation channel of CF₃I leading to CF₂ + IF. A problem might be seen in the endothermicity of reaction (R6), with .³³ However, this appears not to be too relevant for the high temperatures of the present work. Nevertheless, our identification of an additional absorber in Fig. 5–7 remains uncertain, such that more work is required here.

Fig. 5 Absorption signal recorded at 487 nm during the thermal decomposition of CF₃I (1485 ppm of CF₃I in Ar, T = 1197 K, [Ar] = 1.25 × 10⁻⁴ mol cm⁻³, see Section IV).

Fig. 6 Absorption signal recorded at 200 nm during the thermal decomposition of CF₃I (529 ppm of CF₃I in Ar, T = 1188 K, [Ar] = 1.31 × 10⁻⁴ mol cm⁻³, see Section IV).

Fig. 7 Absorption signal recorded at 487 nm during the thermal decomposition of CF₃I in comparison to the simulated I₂ profile (1485 ppm of CF₃I in Ar, T = 1048 K, [Ar] = 1.49 × 10⁻⁴ mol cm⁻³, t = 1 ms corresponds to t = 1.441/k₁ from Section III).

V. Conclusions

After analysis of the decomposition mechanism of CF₃I, the recorded absorption–time profiles of CF₃I of the present work lead to rate constants for the unimolecular dissociation of CF₃I. Within the experimental uncertainty of the C–I bond energy, experiments with various reactant concentrations and different detection methods are in agreement with the theoretically modelled rate constants. The latter confirm that all experiments correspond to the central part of the falloff curves of the unimolecular dissociation. Implementing experimental information on collisional energy transfer of vibrationally highly excited CF₃I^18–21, the modelling then is essentially free from adjustable parameters. In this respect, the present work goes beyond the usual modelling of other unimolecular reaction rate constants.

The present work also provides evidence for the intermediate formation of a species with larger thermal stability than I₂ but having similar spectral features. Tentatively this species is identified to be IF. The importance of various secondary reactions of the decomposition was discussed, but for definite conclusions we need to wait for a confirmation of the identity of IF. The comparison of the present theoretical modelling of falloff curves for CF₃I dissociation with that from ref. 15 showed major differences in the extrapolated limiting low-pressure rate constants. Our detailed analysis such as that described in the ESI† proposes that this is due to the exclusion of centrifugal barriers in ref. 15.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Discussions of this work with K. Hintzer and A. Thaler, technical help by A. I. Maergoiz, and financial support from the Deutsche Forschungsgemeinschaft (Project TR 69/21-1) are gratefully acknowledged.

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Footnote

† Electronic supplementary information (ESI) available: (1) Modelling of rate constants and (2) modelling of spectral properties. See DOI: 10.1039/c9cp04771a

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