Shock wave and modelling study of the dissociation kinetics of C₂F₅I

Abstract

The thermal dissociation of C₂F₅I was studied in shock waves monitoring UV absorption signals from the reactant C₂F₅I and later formed reaction products such as CF, CF₂, and C₂F₄. Temperatures of 950–1500 K, bath gas concentrations of [Ar] = 3 × 10⁻⁵–2 × 10⁻⁴ mol cm⁻³, and reactant concentrations of 100–500 ppm C₂F₅I in Ar were employed. Absorption-time profiles were recorded at selected wavelengths in the range 200–280 nm. It was found that the dissociation of C₂F₅I → C₂F₅ + I was followed by the dissociation C₂F₅ → CF₂ + CF₃, before the dimerization reactions 2CF₂ → C₂F₄ and 2CF₃ → C₂F₆ and a reaction CF₂ + CF₃ → CF + CF₄ set in. The combination of iodine atoms with C₂F₅ and CF₃ had also to be considered. The rate constant of the primary dissociation of C₂F₅I was analyzed in the framework of statistical unimolecular rate theory accompanied by a quantum-chemical characterization of molecular parameters. Rates of secondary reactions were modelled as well. Experimental rate constants for the dissociations of C₂F₅I and C₂F₅ agreed well with the modelling results. The comparably slow dimerization 2CF₂ → C₂F₄ could be followed both by monitoring reactant CF₂ and product C₂F₄ absorption signals, while CF₃ dimerization was too fast to be detected. A competition between the dimerization reactions of CF₂ and CF₃, the recombination of CF₂ and CF₃ forming C₂F₅, and CF-forming processes like CF₂ + CF₃ → CF + CF₄ finally was discussed.

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Introduction

The unimolecular dissociation of perfluoroethyl iodideis of interest for several reasons. On the one hand, like other perfluoroalkyl iodides, C₂F₅I may be of technical use replacing chlorine- and bromine-containing halons, the latter leading to ozone depletion (e.g., ref. 1–4; values in the present article are taken from ref. 5 and 6, except for C₂F₅I and C₂F₄I whose values are estimated by quantum-chemical calculations). On the other hand, it has interesting kinetic aspects. These are the issue of the present article.

There is, at first, the rate of the unimolecular dissociation of C₂F₅I. Next, like the thermal dissociation of (C₂F₅)₃N leading to 3C₂F₅ + N,⁷reaction (1) is a precursor for C₂F₅ which dissociates by the reaction

Under typical shock tube conditions, the products CF₂ and CF₃ of reaction (2) decompose much more slowly than C₂F₅I and C₂F₅, see below. Instead of dissociating, they dimerize by the reactions

CF radicals could be formed in reactions likewhich would lead to the stable product CF₄; CF might dimerize as well, forming the thermally stable C₂F₂ (or C₂F + F), see below. The rate constants of the various steps in the decomposition mechanism of C₂F₅I play a central role for the understanding of halon dissociation in general (see, e.g., ref. 8). It, therefore, appears worthwhile to study C₂F₅I decomposition in detail.

While the unimolecular dissociations of CF₃I and C₃F₇I have been investigated extensively (see, e.g., the shock wave and modelling studies of ref. 3, 9, and 10 for CF₃I and of ref. 4 for C₃F₇I), such work is lacking for C₂F₅I. There have been indirect isothermal, steady-state,^11,12 and CO₂-laser induced¹¹ pyrolysis experiments at moderate temperatures. To our knowledge, however, only a single high-temperature shock wave study has been performed for C₂F₅I.¹³ This used the chemiluminescence process I + I → I₂ + hν to conclude on reaction (1). Because high reactant concentrations (0.2–1% of C₂F₅I in Ar) were employed, secondary reactions such as

or(reaction (6) followed by the fast dissociation of C₂F₄I to C₂F₄ + I and reaction (7) followed by the dissociation of I₂) were suggested to form the I atoms which then were used for detection. Other secondary reactions could not be identified, partly because the also recorded UV absorptions of the parent molecules and reaction products were found to be superimposed. As we have studied UV absorptions of possible reaction products separately before, we started a new approach to C₂F₅I dissociation in shock waves, analyzing superimposed absorption signals from reactants and products in the UV. In comparison to ref. 13, we were able to reduce the reactant concentrations in the shock waves down to 100 ppm in Ar, such that mechanistic aspects of the decomposition could be further investigated under simpler conditions.

The present work should also be seen in relation to dissociation studies of C₂F₅I using other excitation techniques. The UV photolysis of C₂F₅I, e.g., has attracted attention as a fast, direct, dissociation process with high yields of excited ²P_1/2 iodine atoms (e.g., ref. 14–17). The latter was considered useful for the construction of iodine photodissociation lasers (e.g., ref. 18 and 19). The fast dissociation of C₂F₄I to C₂F₄ + I, which had been suggested to follow reaction (6),¹³ has also been accessible.²⁰ UV laser flash photolysis and IR multiphoton excitation studies of C₂F₅I led to information^21,22 on the reverse of reaction (1) near room temperature, i.e. to the recombination

It was the aim of the present work to shed more light on the mechanism of C₂F₅I decomposition under high-temperature and low reactant concentration conditions. A theoretical modelling of the falloff curves for the unimolecular dissociation of C₂F₅I and its reverse reaction (8) was considered helpful for an analysis of the experimental results. As the present work uses UV absorption spectroscopy of the parent molecules and reaction products, quantitative knowledge of several high-temperature absorption coefficients was required. Such information was available from earlier publications referred to later. More information on absorption coefficients of C₂F₅I has been described recently.²³ As reaction (5) may lead to the formation of CF, the dimerization of this species, forming C₂F₂ (or leading to C₂F + F), was also modelled. Likewise, rate constants of other possible secondary reactions such as reactions (6) and (7) were inspected.

Experimental technique and results

Mixtures of 100 and 500 ppm of C₂F₅I in Ar were heated in shock waves. The mixtures (C₂F₅I from abcr with 99% purity and Ar from Air Liquide with 99.9999% purity) were prepared in vessels outside the shock tube before being introduced into the tube. The used tube (length of the test section 4.15 m and inner diameter 9.4 cm) has been described before (e.g.ref. 5, 10, and 23–34). The progress of the reaction was followed through windows placed into the wall of the tube, 5 cm in front of the reflecting end plate. Absorption measurements were made with a high pressure Xe arc lamp (Osram XBO 150 W/4), quartz monochromator (Zeiss M3), photomultiplier, and data acquisition arrangement. Absorption-time profiles were recorded behind incident and reflected waves. The available time for measurements behind the reflected shock was about 1.5 ms. As the observed spectra were all continuous or quasi-continuous, broad spectral widths of about ±1 nm could be used. Selected wavelengths from the range 200–280 nm were monitored. Temperatures for kinetic measurements were between 950 and 1500 K, bath gas concentrations [Ar] between 3 × 10⁻⁵ and 2 × 10⁻⁴ mol cm⁻³.

The experiments led to a diversity of absorption-time profiles. Representative examples are shown in Fig. 1–5. The analysis of the signals used high-temperature absorption cross sections for C₂F₅I and C₂F₅ from ref. 23, for C₂F₄ from ref. 24, for CF₃I (formed by combination of CF₃ with I) from ref. 10 and 25, for CF₃ from ref. 23 and 26, for CF₂ from ref. 24 and 27, and for CF from ref. 28 (representative absorption cross sections at a typical temperature of 1200 K, for orientation, are given in Table 1). In addition, modelled rate constants such as summarized in Table 2 (for their determination, see the following sections and the ESI†) facilitated the analysis. Besides the dissociation reactions, their reverse recombination processes had also to be included. All dissociation and recombination reactions were in their falloff ranges such that suitable falloff expressions of the rate constants (with the parameters given in Table 2) had to be used. Without the mentioned spectroscopic and kinetic input parameters, an interpretation of the signals would have been considerably more difficult.

Fig. 1 Absorption-time profile recorded at 268.5 nm in the decomposition of C₂F₅I (reflected shock wave: T = 1195 K, 500 ppm of C₂F₅I in Ar, [Ar] = 1.3 × 10⁻⁴ mol cm⁻³; OD5 = ln(I₀/I) with light intensity I and path length x = 9.4 cm, see text; : modelled points with data from Tables 1–3, k₅ fitted as k₅ ≈ 2 × k_−2,∞ where k_−2,∞ = k_2,∞/K_2,c, see text).

Fig. 2 As Fig. 1, but recorded at 248 nm (reflected shock wave: T = 1213 K, 530 ppm of C₂F₅I in Ar, [Ar] = 1.3 × 10⁻⁴ mol cm⁻³; : modelled points with data from Tables 1–3, k₅ fitted as k₅ ≈ 1.5 × k_−2,∞ where k_−2,∞ = k_2,∞/K_2,c, see text).

Fig. 3 As Fig. 1, but recorded at 248 nm (reflected shock wave: T = 1117 K, 108 ppm of C₂F₅I in Ar, and [Ar] = 1.4 × 10⁻⁴ mol cm⁻³; : modelled points with data from Tables 1–3, k₃ increased by a factor of 2 and k₅ fitted as k₅ ≈ 10 × k_−2,∞ where k_−2,∞ = k_2,∞/K_2,c, see text).

Fig. 4 As Fig. 1, but recorded at 200 nm (reflected shock wave at t = 0.18 ms: T = 1255 K, 533 ppm of C₂F₅I in Ar, and [Ar] = 1.2 × 10⁻⁴ mol cm⁻³).

Fig. 5 As Fig. 1, but recorded at 280 nm (reflected shock wave: T = 970 K, 497 ppm of C₂F₅I in Ar, [Ar] = 1.6 × 10⁻⁴ mol cm⁻³; : modelled points with data from Tables 1–3, k₁ and K_1,c decreased by a factor of exp(−600 K/T), see text).

Table 1 Selected absorption cross sections σ near T = 1200 K, used for the analysis of Fig. 1–5, see text (* upper limits, estimated for 2000 K)

Species	Wavelength (nm)	σ (cm^2)	Ref.
C2F5I	280	4.1 × 10^−19	23
	268.5	3.3 × 10^−19
C2F4	200	4.5 × 10^−18	24
CF2	280	4.2 × 10^−19	27
	268.5	2.0 × 10^−18
	248	6.8 × 10^−18
	200	3.3 × 10^−23
CF	248	1.0 × 10^−17	28*
	200	7.0 × 10^−17

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Table 2 Modelled rate constants for dissociation reactions and their equilibrium constants (limiting high pressure dissociation rate constants k_∞ in s⁻¹, limiting low pressure dissociation rate constants k₀/[Ar] in cm³ mol⁻¹ s⁻¹, and weak collision center broadening factors F_cent = F^sc_cent × 0.64 to be used in falloff expressions from ref. 39–41, equilibrium constants K_c = k_dis/k_rec in mol cm⁻³, *: experimental adjustment of k_1,∞, k_1,0, and K_1,c possible by adding a factor of exp(−600 K/T), see text)

Reaction	Modelled values	Ref.
(1) C2F5I (+Ar) → C2F5 + I (+Ar)	k 1,∞ = 6.15 × 10^15(T/1000 K)^−0.90 exp(−28 675 K/T), k1,0 = [Ar]8.70 × 10^24(T/1000 K)^−11.92 exp(−33 775 K/T), Fcent = 0.059(1000 K), 0.079(1500 K), K1,c = 6.15 × 10^2(T/1000 K)^−1.36 exp(−28 675 K/T)	Present*
(2) C2F5 (+Ar) → CF2 + CF3 (+Ar)	k 2,∞ = 7.88 × 10^14 exp(−27 181 K/T), k2,0 = [Ar]2.2810^24(T/1000 K)^−14.89 exp(−35 119 K/T), Fcent = 0.054(1000 K), 0.051(1500 K), K2,c = 5.75 × 10^2(T/1000 K)^−0.24 exp(−27 181 K/T)	ESI of 5
(3) C2F4 (+Ar) → 2CF2 (+Ar)	k 3,∞ = 6.0 × 10^15(T/1000 K)^−0.87 exp(−35 050 K/T), k3,0 = [Ar]1.07 × 10^23(T/1000 K)^−9.7 exp(−36 660 K/T), Fcent = 0.083(1000 K), 0.079(1500 K), K3,c = 4.20 × 10^4(T/1000 K)^−2.4 exp(−35 050 K/T)	27 and 29
(4) C2F6 (+Ar) → 2CF3 (+Ar)	k 4,∞ = 1.2 × 10^18(T/1000 K)^−0.52 exp(−49 316 K/T), k4,0 = [Ar]2.61 × 10^27(T/1000 K)^−13.8 exp(−52 289 K/T), Fcent = 0.052(1000 K), 0.041(1500 K), K4,c = 5.94 × 10^4(T/1000 K)^−1.29 exp(−49 316 K/T)	30
(17) C2F2 (+Ar) → 2CF (+Ar)	k 17,∞ = 3.90 × 10^16(T/1000 K)^−0.59 exp(−58 130 K/T), k17,0 = [Ar]1.22 × 10^22(T/1000 K)^−7.10 exp(−59 020 K/T), Fcent = 0.19(1000 K), 0.15(1500 K), K17,c = 3.60 × 10^4(T/1000 K)^−2.15 exp(−58 230 K/T)	Present
(18) CF3I (+Ar) → CF3 + I (+Ar)	k 18,∞ = 5.94 × 10^15(T/1000 K)^−2.20 exp(−28 928 K/T), k18,0 = [Ar]5.44 × 10^21(T/1000 K)^−10.46 exp(−31 358 K/T), Fcent = 0.14(1000 K), 0.13(1500 K), K18,c = 8.80 × 10^2 (T/1000 K)^−2.72 exp(−28 928 K/T)	10

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Fig. 1, first, shows a signal recorded at 268.5 nm, i.e. at the maximum of the room temperature spectrum of C₂F₅I.^14,35,36 The absorption steps at the arrival of the incident and reflected shocks (behind the two Schlieren peaks) allow one²³ to derive the absorption coefficients of C₂F₅I at 691 K (incident shock) and 1195 K (reflected shock; for a quantitative analysis, one has also to account for the absorption in front of the incident shock, using the known room temperature absorption coefficient). At the temperature of the reflected shock, obviously not only the disappearance of C₂F₅I but the appearance of a more strongly absorbing reaction product is observed which then disappears on a longer time scale. The identification of this absorber can be made using the rate constants characterized in Table 2. As k₁ (close to 10⁵ s⁻¹) for Fig. 1 is markedly larger than k₂ (close to 2 × 10⁴ s⁻¹), the decay of C₂F₅I is too fast to be resolved and the rising signal behind the reflected shock must be attributed to CF₂ from reaction (2) (the maximum of CF₂ absorption of is located at 248 nm,^24,27 but the absorption of the broad quasi-continuum with increasing temperature increasingly extends to longer wavelengths, i.e. also to 268.5 nm).

Fig. 2 shows a signal recorded at 248 nm. Under the assumption that each decomposing C₂F₅I by reactions (1) and (2) leads to one CF₂, the initial rate of increase of the absorption behind the reflected shock in Fig. 2 allows one to derive an experimental value of k₂. The detailed analysis (accounting for the Schlieren signal) indeed leads to the modelled value following from Table 2, see below. Besides the initial increase of the signal due to the formation of CF₂, the decay of the signal behind the reflected shock must be explained. One finds that the decay of the CF₂ signal can mostly be attributed to the known dimerization of CF₂ (with rate constants following from Table 2). One, furthermore, observes that the maximum of the signal is markedly smaller than expected for a simple mechanism of reactions (1) and (2) alone. This is attributed to a contribution from reaction (5) which converts CF₂ into less reactive species, see below.

A dependence of the CF₂ signal on the reactant concentration is documented in Fig. 3 where the initial C₂F₅I concentration has been decreased by about a factor of 5 in comparison to Fig. 1 and 2. The initial rate of CF₂ formation again is well explained by that of C₂F₅ dissociation (k₂ ≈ 2 × 10⁴ s⁻¹). The decay of the CF₂ signal on the other hand is markedly slower than that of Fig. 1 and 2, indicating a more complicated kinetics of CF₂ disappearance than explained by dimerization alone, see below.

While a contribution from the parent C₂F₅I to the signal behind the reflected shock at 248 nm is only of minor importance and can be accounted for, one may also look for absorptions from other species. For this reason, we inspected signals at shorter wavelengths. Fig. 4 shows an example recorded at 200 nm. At this wavelength, a contribution of CF₂ to the signal can safely be neglected.²⁴ Instead, the absorption from stronger absorbers, forming during the reaction here dominates. One of these can be identified as C₂F₄.²⁴ First, the rise time of the signal corresponds to the dimerization of CF₂ by reaction (3).^27,29 Second, at higher temperatures where C₂F₄ thermally decomposes, the final signals are consistent with the temperature dependence of the C₂F₄ ⇔ 2CF₂ equilibrium.²⁷ Third, the absolute values and the wavelength dependence of the signals agree with the known results for C₂F₄.²⁴ A second contribution to the signal may arise from the even stronger absorber CF formed by reactions like reaction (5).²⁸ Unfortunately the present work could not provide more insight into the kinetics of CF radicals. It was, therefore, also not clear whether “irregularities” of the signals at late time in Fig. 2 and 4 (after about 1 ms) were due to such reactions, or simply marked the end of the observation time in the shock wave experiments.

In order to record signals with contributions mostly from C₂F₅I, we finally inspected absorption-time profiles at 280 nm, i.e. on the long-wavelength tails of the C₂F₅I and CF₂ absorption continua. Fig. 5 shows a signal recorded for a temperature lower than those used in Fig. 1–4. Here, CF₂ formation is too slow to disturb the absorption signal from C₂F₅I to a major extent, but the decay of C₂F₅I becomes visible.

The overall mechanism of C₂F₅I dissociation, even at reactant concentrations as low as 100 ppm in Ar, apparently was not only determined by the primary first-order dissociation of C₂F₅I, but by several secondary first- and second- order reaction steps and their reverse reactions (equilibrium constants are included in Table 2). A modelling of the corresponding rate constants appeared helpful for a start of the analysis of signals like Fig. 1–5. This modelling is described in the following section (as well as in the ESI†).

Modelling of rate constants for the unimolecular dissociation of C₂F₅I

Our quantum-chemical characterization of the potential energy surface for C₂F₅I dissociation (1) closely followed the procedure outlined for CF₃I dissociation in ref. 10 (and its ESI) and needs not to be repeated here. The derived electronic potential for the C₂F₅–I bond is illustrated in Fig. S1 of the present ESI.† The potential can be approximated by a Morse potential with a Morse parameter β = 1.51 Å⁻¹ (for C₂F₅–I distances larger than 2.2 Å) or β = 1.76 Å⁻¹ (for C₂F₅–I distances larger than 3.25 Å). The quanta of the bending modes of C₂F₅I, which disappear during bond-breaking, decrease exponentially with increasing C₂F₅–I bond length (with decay parameters α = 0.53(±0.01) Å⁻¹, see Fig. S2 of the ESI†). The decrease of the rotational constant (B + C)/2 of the decomposing C₂F₅I is also fitted such as illustrated in Fig. S3 of the ESI.† The latter is required for the determination of the centrifugal barriers which can be represented by E₀(J) ≈ E₀(J = 0) + C_ν[J(J + 1)]^ν with C_ν = hc·1.14 × 10⁻³ cm⁻¹ and ν = 1.17. Neglecting the anisotropy of the potential, i.e. using phase space theory (PST), high pressure recombination rate constants for reaction (8) of k^PST_rec,∞ = (4–6) × 10¹³ cm³ mol⁻¹ s⁻¹ are obtained between 750 and 2000 K (see the modelling results in Table 2). The anisotropy of the potential introduces “rigidity” and reduces k_rec,∞ to values below k^PST_rec,∞. The classical trajectory version of the statistical adiabatic channel model (SACM/CT) of ref. 37 provides a simple approach to express this reduction as a function of the ratio α/β, here shown to be about 0.3 (one notes that this ratio in the present case is somewhat below the “standard value” 0.5,³⁸i.e. it corresponds to a comparably rigid potential). Table 3 shows the results for k_rec,∞ which can be approximated by

k_rec,∞ ≈ 1.0 × 10¹³ (T/1000 K)^0.46 cm³ mol⁻¹ s⁻¹ (9)

Table 3 Modelled rate constants for dissociation and recombination of C₂F₅I, k_dis = k₁ and k_rec = k₈ (k^PST_rec,∞ = k_rec from Phase Space Theory (PST); k^PST_rec,∞ and k_rec,∞ in cm³ mol⁻¹ s⁻¹; k_dis,∞ in s⁻¹; k_dis,0/[Ar] in cm³ mol⁻¹ s⁻¹; F_cent: weak collision center broadening factors; [Ar]_cent in mol cm⁻³: centers of the falloff curves, see text)

T/K	k ^PSTrec,∞	k rec,∞	k dis,∞	k dis,0/[Ar]	F cent	[Ar]cent
750	4.40 × 10^13	8.89 × 10^12	1.99 × 10^−1	4.20 × 10^7	0.063	4.7 × 10^−9
1000	4.76 × 10^13	1.00 × 10^13	2.16 × 10^3	1.86 × 10^10	0.059	1.2 × 10^−7
1500	5.46 × 10^13	1.22 × 10^13	2.14 × 10^7	1.02 × 10^12	0.079	2.1 × 10^−5
2000	6.01 × 10^13	1.39 × 10^13	1.95 × 10^9	1.62 × 10^12	0.12	1.2 × 10^−3

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The corresponding dissociation rate constants k_dis,∞ in Table 2 are represented by

k_dis,∞ ≈ 6.15 × 10¹⁵(T/1000 K)^−0.90 exp(−28 675 K/T) s⁻¹ (10)

It appears worthwhile to compare the modelled high-pressure recombination rate constants for 300 K, i.e. k_rec,∞(300 K) ≈ 5.5(±3) × 10¹² cm³ mol⁻¹ s⁻¹, with the measurements from ref. 21 and 22 which led to a value of 1.2(±0.4) × 10¹³ cm³ mol⁻¹ s⁻¹. Within the estimated uncertainties of either approach, the results appear sufficiently close.

The calculation of the limiting low-pressure rate constant k_dis,0 followed the procedure described in ref. 39 with the required parameters C_ν, ν, and E₀(J) for the centrifugal barriers as given above (for other parameters, see the ESI†). Collision efficiencies and the corresponding average (total) energies transferred per collision 〈ΔE〉 as usual had to be estimated. Like in previous work, we used a value of 〈ΔE〉/hc ≈ −100 cm⁻¹ for a start. This led to

k_dis,0 ≈ [Ar]8.7 × 10²⁴(T/1000 K)^−11.92 exp(−33 775 K/T) cm³ mol⁻¹ s⁻¹ (11)

Falloff expressions for the transition of k₁ from k_dis,0 to k_dis,∞ were expressed in the form proposed in ref. 39–42. The required weak collision “center broadening factors” F_cent = F^sc_cent × 0.64 were estimated with the method of ref. 39–41. Values of F_cent ≈ 0.063, 0.059, 0.079, and 0.12 were derived for T/K = 750, 1000, 1500, and 2000, respectively. The finally obtained falloff curves are shown in Fig. 6. The figure well documents the shift of the falloff curves with temperature. At a bath gas concentration [Ar] = 10⁻⁴ mol cm⁻³ and T ≤ 750 K, the reaction is close to the high-pressure limit, while it is closer to the low-pressure limit at T ≥ 1500 K. Intermediate falloff effects thus are important for all conditions of the present work. Modelled dissociation and recombination rate constants are summarized in Table 3. Values for k_rec,∞ are compared with k^PST_rec,∞, illustrating the effects of the anisotropy of the potential. Furthermore, the positions of the “centers of the falloff curves” [Ar]_cent are given, i.e. the values of [Ar] for which k_dis,0≈ k_dis,∞. The increase of [Ar]_cent with increasing T quantifies the shift of the falloff curves with temperature. It also appears important to estimate the uncertainty of k_dis,∞ caused by the uncertainty of the reaction enthalpy. The modelling of the signal of Fig. 5 and of the rate constants k₁(T) described below suggests an increase of by about 5 kJ mol⁻¹ which adds a factor of about exp(−600 K/T) to eqn (10) and (11) as well as K_1,c in Table 2. Finally, it appears of interest to compare the present modelling results for k₁ with values obtained from the iodine chemiluminescence experiments of ref. 13. The values for k₁ from the latter work at 1100 K are about a factor of two larger than the present modelling whereas they nearly agree near 1300 K.

Fig. 6 Modelled falloff curves for the unimolecular dissociation of C₂F₅I in Ar (calculations for 750, 1000, 1500, and 2000 K from bottom to top; see text and ESI†).

Modelling of rate constants for secondary reactions

In this section we describe modelling results for reactions which may play a role as secondary processes in the decomposition mechanism of C₂F₅I. As the falloff curves for the dissociation reactions of C₂F₄, C₂F₅, C₂F₆, and CF₃I and their reverse recombination (or dimerization) reactions had been characterized before, they need not to be described here again (see their parameters in Table 2). We only performed a further modelling of C₂F₂ dissociation and the reverse CF dimerization rates. These data are needed in case that CF is formed by some secondary reactions (details of this modelling are described in the ESI† and the results are included in Table 2). CF is a particularly strong absorber over the wavelength range 200–280 nm studied in the present work, such that eventual contributions from CF to the recorded signals had to be carefully considered. CF, e.g., could be formed by reaction (5); high-energy dissociation channels of C₂F₄, C₂F₅, and C₂F₆, however, could also play some role. For this reason, we determined minimum-energy path (MEP) potentials of the corresponding processes using the quantum-chemical techniques mentioned above. Fig. 7 shows the results for reaction (5) and the dissociation of C₂F₅. The calculations first show that the MEP pathway from CF₂ + CF₃ through bound C₂F₅ to CF + CF₄ involves a high energy barrier (TS) of 224.6 kJ mol⁻¹. This would rule out reaction (5) as a pathway for CF formation. However, one may imagine that the exothermic reaction proceeds as a roaming radical process (analogous to processes described in ref. 43–45), skirting “outside” along the barrier of the TS and avoiding the passage of the C₂F₅ intermediate. While this looks like an attractive possibility, its confirmation by trajectory calculations on a full potential for C₂F₅ is not within the scope of the present article.

Fig. 7 Schematic energy diagram for reactions (2) and (5) (energies in kJ mol⁻¹; from ab initio composite G4 model and Intrinsic Reaction Coordinate (IRC) calculations; see text and ESI†).

A high-energy pathway of C₂F₄ dissociation forming CF under the present conditions apparently is too endothermic (, see the MEP potential of Fig. S13 of the ESI†). On the other hand, the exothermic pathway , followed by reaction (5)i.e. by , could also lead to CF (see the MEP potential for CF₃ + CF₃ in the ESI,† Fig. S14). The formation of some CF in the decomposition mechanism thus also appears possible. It should finally be mentioned that absorption-time profiles like Fig. 4 were also observed in the study of the decomposition of CF₃I (see Fig. 6 of ref. 10); these signals were tentatively attributed to the formation of IF. However, an interpretation analogous to that from the present work presents a more attractive alternative. If CF is formed, besides the dimerization 2CF → C₂F₂ a reaction 2CF → C₂F + F should also be considered (see details in ESI†-III).

Besides pathways for CF formation and rates for CF dimerization, we also modelled the bimolecular reactions (6) and (7) between the parent C₂F₅I and its dissociation products C₂F₅ and I. These reactions could be important for higher reactant concentrations and they were used for the observation of the C₂F₅I decomposition reaction by detection of I₂ in ref. 13, see above. Reaction (6) could proceed on the two exothermic pathways

but in both cases high energy barriers TS are involved. The calculations described in the ESI† led to activation enthalpies of 164.8 kJ mol⁻¹ for reaction (12) and 181.1 kJ mol⁻¹ for reaction (13). TST calculations of the rate constants were represented by

k₁₂ ≈ 2.7 × 10¹⁰(T/1000 K)^3.1 exp(−1985 K/T) cm³ mol⁻¹ s⁻¹ (14)

k₁₃ ≈ 1.2 × 10¹¹(T/1000 K)^3.1 exp(−21850 K/T) cm³ mol⁻¹ s⁻¹ (15)

corresponding to k₁₂ = 6.5 × 10¹ cm³ mol⁻¹ s⁻¹ and k₁₃ = 4.0 × 10¹ cm³ mol⁻¹ s⁻¹ at T = 1000 K. In contrast to these reactions, for reaction (7) between I and C₂F₅I no activation barrier was found beyond the endothermicity. This is consistent with the experiments of ref. 11, 12, and 46 which determined an activation energy close to zero for the reverse reaction I₂ + C₂F₅ → I + C₂F₅I. Converting the experimental results for this reaction with the equilibrium constants led to

k₇ ≈ 3.6 × 10¹³ exp(−7460 K/T) cm³ mol⁻¹ s⁻¹ (16)

corresponding to k₇ ≈ 2 × 10¹⁰ cm³ mol⁻¹ s⁻¹ at T = 1000 K. Clearly reaction (6) thus can be neglected, while reaction (7) must be accounted for in experiments using larger concentrations than those of the present work.

Analysis of experimental absorption profiles

As emphasized before, the analysis of experimental absorption-time profiles is greatly facilitated by the modelling results described in the two previous sections. In the following this will be demonstrated for the shown examples of experimental signals. As the considered dissociation and the reverse recombination reactions are all in their falloff ranges, the falloff expressions from ref. 39–41 for the [Ar]-dependence of the rate constants were used. The required falloff parameters and equilibrium constants K_i,c were taken from Tables 2 and 3.

For the lowest temperatures of the present study (and the given [Ar]), k₁ exceeds k₂ (e.g., k₁ = 6.7 × 10² s⁻¹vs. k₂ = 2.0 × 10² s⁻¹ for Fig. 5). The signal of Fig. 5 at 280 nm, therefore, is dominated by the faster decay of C₂F₅I and not by the much slower formation of CF₂. Fig. 5 includes a modelled absorption-time profile, accounting for the contributions from C₂F₅I and CF₂. In spite of the superposition of the two absorptions, signals like Fig. 5 can be used to derive experimental values of k₁ independent of the precise value of k₂. One should note, however, that in later stages of the reaction one must account for the onset of the recombination reaction (8), i.e. of C₂F₅ + I → C₂F₅I. This can be done with the help of the equilibrium constant K_1,c given in Table 2. Within the relatively large experimental uncertainty (because of the superposition of the two absorptions estimated to be about a factor of two), the derived values of k₁ agree with the [Ar]-dependent modelling results such as illustrated by the Arrhenius plot of Fig. 8. An improved fit was obtained (both in Fig. 5 and 8) if was increased from the value calculated in the present work (see the ESI†) by about 5 kJ mol⁻¹. One should mention one further complication: according to the equilibrium constants from Table 2, one would have expected a dissociation of only a few percent of C₂F₅I until equilibrium in Fig. 5 is reached whereas the signal decays to smaller values. This observation, however, is explained by the onset of reactions (2) and (5), and possibly some contribution from reaction (6).

Fig. 8 Pseudo-first order rate constants k₁ of the unimolecular dissociation of C₂F₅I at [Ar] = 1.4 × 10⁻⁴ mol cm⁻³ (full line: modelling results from Tables 1–3, curve a for , curve b for ; symbols: examples of experimental results from the present work with estimated error bars, see text).

Observations at 268.5 nm, such as illustrated in Fig. 1, like in Fig. 5 are characterized by the superposition of absorptions from C₂F₅I and CF₂. As the absorption cross sections of both species are known (see Table 1), the signals nevertheless can be simulated. With the modelled values for k₁ and k₂ (as well as the other rate constants from Table 1, in particular k₃), results such as included in Fig. 1 are obtained, validating the given interpretation of the signals.

At 248 nm the absorption cross section of CF₂ by far exceeds that of C₂F₅I. As C₂F₅I decomposes much more rapidly than CF₂, the formation and consumption of the latter species can well be studied without interference from C₂F₅I. Assuming that one C₂F₅ is produced per one dissociating C₂F₅I, the initial rise of the CF₂ signal can be attributed to CF₂ formation by reaction (2) alone. The modelling of the complete mechanism also allows one to predict the maximum of the signal. With reactions (1)–(4) one predicts a larger signal than observed. This can be attributed to reaction (5) which efficiently converts CF₂ and CF₃ into the less active species CF and CF₄. The reduction of the maximum of the signals allows one to fit k₅. One obtains values of the order of the limiting high pressure rate constant for the recombination of CF₂ and CF₃ forming C₂F₅ (e.g., for Fig. 2, k₅ ≈ 2 × k_−2,∞ where k_−2,∞= k_2,∞/K_2,c; unfortunately the fit of k₅ is markedly influenced by uncertainties in k₁, k₂, k₃, and k₄, such that more precise determinations have to wait for studies in simpler reaction systems; so far the uncertainty of k₅ is estimated to be about a factor of 4).

The contribution of reaction (5) weakens when the reactant concentration is further decreased. Fig. 3 shows an example with a reactant concentration as low as about 100 ppm. The mechanism here indeed is dominated by reactions (1)–(4). Measurements at 248 nm were also performed behind incident shock waves, such that [Ar] could be varied between 2 × 10⁻⁵ and 2 × 10⁻⁴ mol cm⁻³. The comparison between experimental and modelled rate constants in the falloff range of reaction (2) is illustrated in Fig. 9 for low and high [Ar]. An agreement with the modelled rate constants within about a factor of 2 was obtained, similar to that of Fig. 8.

Fig. 9 Pseudo-first order rate constants k₂ of the unimolecular dissociation of C₂F₅ (2) (full line: modelling results for [Ar] = 1.5 × 10⁻⁴ mol cm⁻³, dashed line: modelling results for [Ar] = 2.8 × 10⁻⁵ mol cm⁻³, see Table 2 and ref. 7; symbols: experimental results from the present work with estimated error bars, see text; open circles for [Ar] = 2.8 × 10⁻⁵ mol cm⁻³, filled circles for [Ar] = 1.5 × 10⁻⁴ mol cm⁻³).

While the signals of Fig. 1, 3 and 5 could well be modelled with the data from Tables 1–3 and fitted values of k₅, the modelling of Fig. 4 met with difficulties. Although the time dependence of the increasing signal at 200 nm corresponds well to the formation of C₂F₄ by the dimerization reaction (3), the signal is larger than explained by C₂F₄ formation alone. Obviously, there is an important, additional, contribution to the signal from the strong absorber CF formed by reaction (5). As only upper limits of the absorption cross section of CF at 200 nm are available (for temperatures near 2000 K) and more precise values of k₅ are needed, a modelling of the signal of Fig. 4 does not yet appear warranted. This also concerns the “irregularities” of the signal after about 1 ms (mentioned for Fig. 2 above; one should also mention that the step of the signal at the arrival of the reflected shock wave is due to C₂F₅I from an absorption band located at wavelengths below 200 nm²³). Because of these complications, the present reaction system did not appear suitable for further studies of CF reactions.

Conclusions

The described UV absorption study has provided insight into the dissociation mechanism of C₂F₅I. It has allowed us to analyze the absorption-time profiles of the dissociating C₂F₅I and of reaction products like CF, CF₂ and C₂F₄. As the absorptions of these species are all superimposed, modelled rate constants and separately determined absorption cross sections facilitated the analysis of the recorded signals. The diversity of the signals allowed for a validation of the modelled rate constants and the decomposition mechanism. The detection of iodine atoms by ARAS (atomic resonance absorption spectroscopy) like in ref. 3 and 4 (studying the dissociations of CF₃I and C₃F₇I), would have allowed to work with even lower reactant concentrations than the present UV absorption technique and provided a more direct access to the unimolecular dissociation of C₂F₅I. However, monitoring UV absorption signals of other species at higher reactant concentrations has provided insight into the decomposition mechanism and its secondary reactions.

A number of points deserve particular mention: (i) even under the low concentration conditions of the present work, the reverse of all dissociation reactions had to be included; (ii) falloff effects of all dissociation and recombination reactions had to be accounted for; (iii) the dominant absorption contributions came from C₂F₅I, CF₂, C₂F₄, and CF, however, with relative importance varying with wavelength and temperature; (iv) CF probably was formed by a roaming radical process CF₂ + CF₃ → CF + CF₄ (5) bypassing the bound C₂F₅ intermediate (with a rate constant of the order of, but somewhat larger than, the limiting high pressure rate constant for the recombination of CF₂ and CF₃ forming C₂F₅); (v) CF apparently dimerizes to C₂F₂. (vi) besides I atoms, the most stable end products of the decomposition under the conditions of the described work probably are CF₄ and C₂F₂.

The present study illustrates again the benefit of combining kinetic measurements with rate constant modellings. Experimentally determined rate constants for the dissociations of C₂F₅I and C₂F₅ were shown to agree well with modelled values which then validates the use of the modelled rate constants for extrapolation into unexplored ranges.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Financial support of this work by the Deutsche Forschungsgemeinschaft (Project TR 69/21-3) is gratefully acknowledged. Open Access funding provided by the Max Planck Society.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0cp06414a

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