Xenon monochloride
A corresponding reaction could be found for the Cl Termolecular reactionsThey are essentially produced in ternary mixtures and are of the type: Xe** + Cl The rate constant kc is given in table 15. Notice only the processes where M=Ar are negligible.
As for helium, there are two reactions: Xe* + Cl + He → XeCl Xe** + Cl + He → XeCl The rate constants are respectively, 10−27 cm6s−1 and 3×10−27 cm6s−1.[134] There also exist data where the xenon atoms are at the ground state: Xe + Cl + M → XeCl (X) + M where M = Ne or Xe In both cases, the rate constant is: 1.2×10−33 cm6s−1.[135] Other reactionsChlorine, Cl Xe + Cl Xe* + Cl As the sublimation temperature of XrCl Some authors have proposed increasing the temperature to make XeCl XeCl Xe* + XeCl The temperature increase procures two advantages: to eliminate the parasitic laser phenomenon and increase XrCl production. However, the increase should not be of much importance so that XeCl In ternary mixtures, RgCl exciplexes could be synthesized, possibly leading to the formation of XeCl RgCl* + Xe → XeCl Inversely, RgCl synthesis consumes the available chlorine reducing the rate of XeCl production. The laser quality may be negatively affected as was the case with krypton.[139] This review will be limited to synthetic reactions of XeCl Ion recombinationAccording to several authors[115][140][141] bimolecular reactions (Xe+ + Cl− Ternary reactions are typically: Xe+ + Cl− Xe+ RgXe+ Xenon ions are synthesized directly in the discharge or through successive reactions that involve Rg+, Rg2+ as well as other ionic or excited species. Figure 1 gives an example where Rg=Ne and figure 6 where Rg=He.[116][119][142][130][143][144] The Cl− HCl(v) + e− → H + Cl− In that same case, the rate constant (AD) depends on the energy distribution of the electrons as illustrated in Figure 4. The third element Rg is passive chemically. It only serve to stabilize the reaction.[145] Therefore, the authors only took the recombination rates of the positive and negative ions into consideration. These vary in a significant way with the total pressure of the gaseous mixture, the buffer gas and temperature. Reactions (3) and (4) were experimentally demonstrated for all the rare gases. Figure 7 and Figure 8 show the influence of the buffer gas and pressure on the rate of recombination of these reactions when helium and then neon are utilized as buffer gases. This rate of recombination is of the same order of magnitude in both cases, of about some 10−6 cm3s−1. Apparently the influence of temperature has only been studied for neon. (See Figure 9.) The rate of recombination α3 in reaction (3) is at maximum at 180K for an absolute pressure of 294.2 kPa.[146] α3 is therefore 4.2×10−6 cm3s−1. The more refined analysis of reaction (4) was carried out by Bates et Morgan.[147] who found that the Monte-Carlo method, Flannery's equation and Langevin's theory can give good results only when the pressure is above 1 atm. This is the norm for lasers. The proposed "tidal" theory agrees with the experimental measurements of Mezyk et al.[140] which is evident in Figure 10. The rate of recombination α4 for reaction (4) is of the same order of magnitude as α3. Reaction (5) is only observed when Rg is neon or argon. For this reaction, the evolution of the rate of recombination α5 in the presence of pressurized neon is shown in figure 6. Imada et al.[148] studied the influence of temperature for a fixed total pressure of 294 kPa. The maximum value of α5 is obtained at 120K and α5 = 7.5×10−6 cm3s−1. For argon only two estimations are available at room temperature. At a pressure of 2 atm, α5 = 2.10−6 cm3s−1[149] and at a pressure of 1 atm, α5 is 1×10−6 cm3s−1.[65] Reaction (5) does not favor a transitory complex RgXeCl RgXe+ + Cl− On the contrary, the principal synthetic pathway is given by: RgXe+ + Cl− Kannari et al..[142] estimated the contribution of each of the three recombination and harpooning reactions for three types of mixtures. The results are shown in Table 16. Reaction (3) provides the bulk of the exciplex molecules and generally the harpooning reactions play a secondary role. When helium is used, in contrast, the harpooning reactions contributes about 10–15% of XeCl
In table 16, the column named "others" shows 5.8% for neon, meaning that other recombination pathways are possible. Xe3+ ions are synthesized in the gaseous mixtures used in lasers. These ions react with Cl-10− Xe+* ions react with Cl− The first estimate of the ionic pathways was made by Tysone and Hoffman[155] who suggested 76% for states B and 24% for states C. Successively, the buffer gases are neon, argon and krypton. Ohwa and Kushner[156] published similar values: 77% for states B and 23% for states C. They used a quaternary mixture containing a buffer gas (using neon) from hydrogen, H2. A recent and more detailed study was conducted by Tsuji et al.[141] in a mixture of helium as buffer gas. They found that: – States D are especially formed from Xe+ ion, (2P1/2) ; – States B and C are exclusively produced from Xe+ ion (2P3/2) in the following proportions: States B – 62.6% and States C – 38.4%. The rate of production of XeCl In laboratory experiments, the number of the Xe+(2P1/2) and Xe+(2P3/2) states are the same. In addition, the rate constants of reaction (3) relative to these two states of xenon are similar. However, under these conditions, the number of states D formed is very low with respect to the number of states B and C. The rate of XeCl(D) formation with respect to XeCl(B, C) is estimated at 0.033±0.006. The faster dissociation of [Xe+(2P1/2)Cl− Pathways of decompositionRadiationEmission spectraThe corresponding spectra demonstrated in Figure 11 was observed by virtually all authors who studied mixtures that were based on xenon and a chlorine donor. Two theoretical studies have enabled identification of the emission spectra.[42][49] Five transitions have heightened intensities that correspond to ΔΩ = 0 i.e., a parallel polarization to the internuclear axis. The starting states are always ionic and the product states are covalent. The characteristics of these emissions are as shown in Table 17.
The most probable UV transitions are the B→X and D→X. They have the Σ→Σ type. The other transitions, B→A, C→A and D→A, have the nature Π→Π and are much less probable.[73] Other theoretically weaker transitions have not yet resulted in an observation with the exception of Hay and Dunning,[49] who made provisions for four transitions that are perpendicularly polarized at the internuclear axis; in other words, with ΔΩ = ±1. Only Ewing and Brau[89] noted an emission centered at 425 nm attributed to a 2Σ→2Π transition. Finally, Krauss[73] suggested the possibility of an emission of the D→B type whose transition period is itself very weak. Table 6 places this at 931 nm. The principal emissions were observed and reported as in Table 17. The B→X line is observed at 308 nm (Figure 11) while the theoretical prediction of its existence was clearly weak. This is the narrowest emission and the final state shows a somewhat shallow potential well. Just like the rare gas halides, this emission has the strongest transition period. That is why it is the preferred emission in XeCl lasers.[4] Experimentally, the (C→A) and (B→A) lines overlap,[59] producing a continuum centered at 345 nm, often of low amplitude as can be observed in Figure 11. The width of the emission depends on the transition tending to a strongly repulsive state. Koltz et al. placed this continuum at between 312 and 460 nm.[50] The weak observed intensities are attributed to the weakness of the probabilities of the transition of the two emissions opposite that of the B→X and by the small amounts of states C formed with respect to states B as was previously seen. Other authors have called attention to the absorption phenomena of molecule Xe The (D→X) transition centered at 235.5 nm has not been systematically observed. The corresponding line appears weak as in the case in Figure 12. Its optical width is similar to that of (B→X) emission because it leads to the same weakly bound state of X.[53] In contrast, the relative intensity of the (B→X) and (D→X) emissions considerably vary from one author to the other: ID→X/IB→X = 1/3 by Shuker,[53] 1/25 to 1/50 by Sur et al.[81] and 0.14 by Taylor et al..[160] The latter authors noted that the relation is pressure-independent. It remains unlikely that a laser could be developed using this transition as Shuker had predicted.[53] The spectra did not show any D→A emission. Nevertheless, Hassal et Ballik[100] saw a line at 246 nm with very weak intensity (figure 12) without attributing it to the transition under consideration. State D emissions are negligible for XeCl spectroscopy. Attributing the absence of D→A as for D→B to the weakly associated transition probability,[42][49][73] the same cannot be said for D→X. From Table 17, the D→X emission should be of lesser intensity than B→X. In this case, the possible explanation could be due to the weak production of state D, either by the ionic pathway[141] or by the harpoon reaction using states Xe(3P).[97] The principal path of XeCl These emissions are more or less degraded for short wavelengths as the emission spectrum of the (B→X) line shows in figure 13. A corresponding oscillation phenomenon with the same wavelength was observed in the absorption spectra.[52] Besides, the (D→X) emission has the same line structure as (B→X).[81] The width and oscillatory nature of these lines are bound to the existence of transitions arising from high vibrational levels of excited radiative states.[50][74][92] The vibrational excitation is a result of the energy left after exciplex molecule formation. This energy depends on both the state of the xenon atom/ion involved in the reaction and the halogen donor.[58][74][115] For the 345 nm emission, the transitions at a high vibrational level are more dispersed towards the red region for C→A3/2 than for B→A1/2 because the repulsive barrier of A3/2 is steeper and closer to the higher state of the emission than is A1/2.[74] The oscillatory nature of these spectra tends to disappear with an increase of pressure, showing only the peaks arising from the v≤2 level when the pressure is above 1 atm. This shows that the vibrational relaxation effectively depopulates the highest vibrational levels.[10][92] On the other hand, the disappearance of the elevated levels is faster for state B than for state C because state C has a much longer lifetime.[74] The vibrational relaxation of states B and C play an important role in the chemical kinetics of XeCl lasers. Beyond 5 atm, these lines increase in width, possibly due to collisional enlargement induced by rays or due to the entire rotational structure.[161] The isotopic effects are negligible for xenon but marked for chlorine. The vibrational lines associated with the heaviest isotope 37Cl are lightly displaced towards the greatest wavelengths. For example, the gap reads 1.51Å for the 4-0 line of B→X.[55] Radiative lifetimes of excited speciesValues for states B, C and D are shown in Table 18 for the vibrational level v=0. These are states B and C which have resulted in more determinations.
In state B, two values are statistically distant from the others.[67][162] They correspond to the oldest measurements. Without taking them into account, the confidence interval obtained in ns is: 8<τB<12.3. For state C, the dispersion is more important. Grieneisen et al.'s determination[67] is still statistically distant from the others as well as the two theoretical values[42][49] along with a measurement obtained at the solid state.[76] When the above is disregarded, the confidence interval, in ns, then becomes: 129.1<τC<135.9. Using average values, the relation τB/τC is 0.0764. It is adequately comparable with a direct measure which is 0.087 ± 0.009.[64] This relation is important because it plays an important role in the vibrational relaxation of states B and C. A systematic study of the lifetimes of several vibrational levels (v≤136) of states B and C was conducted as reported in Table 19.[163]
Lifetimes increase by a factor of 4 when v goes from 0 to 100. A graphical extrapolation of the data relative to state B is shown in Figure 14.  For state D, only three determinations are relatively close to one another. At the gaseous state, Shuker[53] noted that D→X emission has a time-based dependence similar to B→X emission, which is in line with the previous magnitudes as the lifetime of the B state is of the order of 10 ns. However, other measures are necessary to precisely value τD. The collisional pathwayThe influences of xenon and HCl will be discussed first, followed by the role of the diverse buffer gases and of the chlorine donors. Destruction of the XeCl | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Ref | kH | kX | kDX | kM | ke |
|---|---|---|---|---|---|
| [164] | 1.4 × 10−9 (± 40%) | 3.2 × 10−11 (± 35%) | |||
| [61] | (6.3 ± 0.5) × 10−10 | (2.3 ± 0.3) × 10−11 | |||
| [130] | 4 × 10−8 | ||||
| [71] | 0.4 × 10−11 | 1.3 × 10−30 | |||
| [70] | (7.3 ± 0.1) × 10−10 | < 4 × 10−12 | (1.53 ± 0.1) × 10−30 | ||
| [62] | (5.0+3.0−2.0) × 10−12 | (13.0 ± 4.0) × 10−31 | |||
| [165] | 7.3 × 10−31 | ||||
| [166] | 1.16 × 10−7 | ||||
| [155] | 1.7 × 10−9 | 4 × 10−31 | 1.2 × 10−7 | ||
| [167] | (7.3 ± 0.1) × 10−10 | ||||
| [131] | 1.5 × 10−30 | ||||
| [162] | 7.7 × 10−10 | 2.1 × 10−12 | 1 × 10−30 | ||
| [16] | (3.8 ± 2.3) × 10−10 | (4 ± 19) × 10−13 | (1.0 ± 0.4) × 10−30 | (4.6 ± 2.1) × 10−29 | |
| [168] | 1.5 × 10−31 | ||||
| [135] | 5 × 10−31 | 2 × 10−8 | |||
| [116] | 3 × 10−7 | ||||
| [169] | 3 × 10−8 | ||||
| [170] | 2 × 10−7 | ||||
| [119] | 1 × 10−7 |
Reaction (9) has been observed only once, recently.[16] Comparison data are therefore not available. In contrast, the other reactions have been repeatedly observed and quantified.
For kH, three measures are statistically distant from the others.[16][155][164] The last (older) two are superior to the others. The first, a recent measure, is the only experiment which proved process (9) which had been neglected. Measurements made by Rives et al.,[16] kH must be multiplied by 2 which puts them at the same level as the other values. Taking reaction (9) into account, the set of values of kH must be revised downward except for Rives et al..[16] A confidence interval is difficult to obtain in these conditions.
For kX, a statistical analysis is very difficult because of the high dispersion of significant absolute values of doubled uncertainties. Lorents[70] provided only an upper limit. Rives et al.[16] results leave open to question whether this process is computable, considering its weak rate constant. Statistically, kX, should not surpass 6.12×10−12 cm3s−1.[61] One other (old) measure,[164] had already provided an erroneous value for kH. Another measure[61] was strongly revised downwards six years later.[62]
Reaction (8) which does not lead to the production of Xe
2Cl* is of negligible importance.[62][111] The measurements given for kDX are well dispersed and the confidence interval contains only three values.[16][162][165] Two of the excluded measurements are of doubtful estimations,[135][168] while the others are correspondingly direct measures[62][70][71][131][155] that provided good results. Hanging over kDX is a great uncertainty, but the average value is representative of the overall results, that is, 9.1×10−31 cm6s−1.
The measured values of ke display a strong dispersion. Only four values are statistically close[119][130][155][166] The average value of 9.6×10−8 cm3s−1 is relatively close to the only direct measure.[166]
Lou[171] also suggested other products for reaction (10):
XeCl
* + e− → Xe+ + Cl− (ke1 = 1.8×10−7 cm3s−1) or → Xe* + Cl + e− (ke2 = 1.2×10−7 cm3s−1)
Some differences were noticed for reactions of type (6) accounting for the vibrational levels of the collision partners:
XeCl
*(v=0) + HCl(v=1) → Xe + HCl + Cl + Cl (6a) with rate constant of kHa
XeCl
*(v=0) + HCl(v=2) → Xe + HCl + Cl + Cl (6b) with rate constant of kHb
XeCl(B,C;v≠0) + HCl(v=0) → Other products and not XeCl (6c) with rate constant of kHc
The values of the rate constants are summarized in Table 21. They are well dispersed and do not correspond to any direct measurement. These values are specifically based on analogous estimations.
Table 21. Values of kHa, kHb, kHc in cm3s−1. Ref kHa kHb kHc [116] 7.7 × 10−10 [172] 6.3 × 10−10 [171] 1.4 × 10−9 [143] 7.7 × 10−9 7.7 × 10−9 [152] 7.7 × 10−10 [156] 6.3 × 10−10 [173] 6.3 × 10−10
Reactions that correspond to reactions (6) and (7) are evident when XeCl is in the ground state of X(v=0). These phenomena affect laser performance and are therefore important. The rate constants are assembled in Table 22. These rates do not vary with the vibrational level of the colliding molecules. Only one direct measurement exists;[30] the others are estimates.
Table 22. Rate constants of disappearance in cm3s−1 through binary collisions. The results are relative to XeCl(X, v = 0) along with another partner, either of Xe, HCl and an electron. Ref Xe HCl e− [30] (5.6 ± 0.8) × 10−12 (2.2 ± 0.5) × 10−11 [121] 2.2 × 10−11 5.6 × 10−10 [135] 8 × 10−12 2 × 10−8 [171] 7 × 10−8
Role of the buffer gas
The addition of a third gas in significant quantities also affects the kinetics of disappearance of XeCl(B,C). It induces reactions which are similar to those produced by xenon:
Double collision (11) : XeCl(B,C) + Rg → Xe + Cl + Rg rate constant of k11
Triple collision (12) : XeCl(B,C) + 2 Rg → Xe + Cl + 2 Rg rate constant of k12
Mixed triple collision (13) : XeCl(B,C) + Xe + Rg → 2 Xe + Cl + Rg rate constant of k13
The rate constants of the three processes are grouped in tables 23–25.
Table 23. Values of k11 in cm3s−1 for the different rare gases. Ref He Ne Ar Kr [62] (1.1 ± 0.2) × 10−12 (0.76 ±0.15) × 10−12 (1.8 ± 0.5) × 10−12 (4.0 ± 0.6) × 10−12 [168] 5 × 10−13 [174] 1 × 10−12 [164] (1.0 ± 0.3) × 10−12 [162] 3.3 × 10−13 [156] 10−11 [175] < 2 × 10−13
Reactions (11) and (13) are always important while reaction (12) has a negligible contribution. The results are greatly dispersed. Differences may reach orders of magnitude. Four references[62][70][164][175] have resulted in direct measurements of reaction rates. Others are estimates. These are based on correspondences and only indicative. No information is available for krypton.
Table 24. Values of k12 in cm6s−1 for different rare gases. Ref He Ne Ar Kr [175] < 3 × 10−33 [168] 5 × 10−34 [176] 5 × 10−32 [152] 1 × 10−33 [164] < 1 × 10−33 [156] 1 × 10−34
Competitive reactions are evident for the totality of these reactions.
Table 25. Values of k13 in cm6s−1 for different rare gases. Ref He Ne Ar Kr [175] (3.8 ± 0.2) × 10−30 [62] (2.4 ± 0.5) × 10−31 (7.4 ± 1.5) × 10−31 (8.9 ± 1.9) × 10−31 (9.9 ± 1.9) × 10−31 [70] (1.01 ± 0.05) × 10−30 [168] 1.5 × 10−32 1.5 × 10−31 [156] 5 × 10−32 [130] 1 × 10−31 [176] 1.5 × 10−31 [119] 2 × 10−31
The reactions of (11) are competitive for displacement reactions. In this case, the products are RgCl(B). They have only been observed in the case where Rg = Kr:[138]
XeCl
* + Kr → KrCl + Xe
The rate constant is 0.7×10−9 cm3s−1.[139] Therefore, this reaction is more effective than quenching. It plays an important role in laser kinetics. It is also as fast as the process of creation of XeCl
* by harpoon reaction. Table 20 concerns one of the principal pathways of destruction of the exciplex molecule.
For Brashears et al.,[177] it is possible to obtain the triatomic complex, RgXeCl
*, as product. This is a competitive reaction when collisions that produce dissociated atoms occur. Emissions of KrXeCl at 370 nm have been observed,[177] along with ArXeCl at 326 nm[178] and NeXeCl at 434 nm.[91] The rate constants have not been measured, except for Rg=Kr, which is 9×10−33 cm6s−1.[62]
However, the creation of ArXeCl seems to be preferential by a competitive reaction (13):
Xe* + Ar + Xe → ArXeCl
*
The rate constant is 4×10−30 cm6s−1.[9] It is then of the same order of magnitude as (13).
However, the synthesis of the Xe
2Cl* trimer is the most frequent competitive reaction of (13).
For helium, Baginskii et al.[174] provided a solution using Xe*
2 + Cl + He of which the rate constant is 1.5×10−31 cm6s−1.
A corresponding reaction for (11) was demonstrated for XeCl at the ground state. The rate constants are summarized in Table 26. The measurements are greatly dispersed (only one is direct) and data on krypton are absent.[30] The others are based, more or less, on estimates. Amongst these, one[179] is statistically distant from the others. On using neon, the rate constant for XeCl(X, v=1) has been estimated as 1×10−11 cm3s−1.[156]
Table 26. Rate constants of disappearance in cm3s−1 through binary collisions relative to XeCl(X, v=0) for various buffer gases. Ref He Ne Ar Kr [119] 5 × 10−12 [173] 9.8 × 10−11 [180] 3 × 10−12 [30] (1.0 ± 0.15) × 10−13 (0.6 ± 0.06) × 10−13 [116] 1 × 10−11 [171] 1 × 10−12 [135] 8 × 10−12 [179] 5 × 10−11
Other chlorine donors and other reactions
The main reactions are those corresponding to reaction (6):
XeCl
* + RCl → Other products and not XeCl (14) rate constant of kR
The values of the rate constants through RCl = Cl
2 or CCl
4 are summarized in table 27. The three chlorine donors studied (HCl, Cl
2 and CCl
4) have rates of quenching of the same order of magnitude.
Table 27. Rate constants in cm3s−1 relative to reactions (14) for XeCl (B, C ; v’ = 0,1). Ref Cl
2CCl
4[61] (4.3 ± 0.2) × 10−10 [70] (5.6 ± 0.25) × 10−10 [165] 5 × 10−10 [131] 5.9 × 10−10 [71] 5.8 × 10−10 [175] (4.6 ± 0.2) × 10−10
All the measurements in Table 27 were experimental. For chlorine, only one (recent) value is statistically distant from the others.[61] The absolute difference is not very great versus the other determinations. An average value for kR for chlorine is 5×10−10 cm3s−1, which is very close to a measure relative to CCl
4.
For chlorine, Grieneisen et al.[67] pointed to two different values for the rate constant for states B and C. They were respectively estimated as (8.8 ± 1.5)×10−10 cm3s−1 and (3.3 ± 0.3)×10−10 cm3s−1. This is a direct measure of the process of destruction through binary collision with Cl
2 that includes all the phenomena and not just quenching. As states B and C are energetically close, collisional coupling is acting on the two states. A similar result for xenon seems to reinforce this hypothesis.
Some atoms of free chlorine exist in the conditions which matter for lasers. The following quenching reactions is provided for:
XeCl
* + Cl → Xe + 2Cl
Two authors have estimated the rate constant: 1.4×10−9 cm3s−1[119] and 8×10−10 cm3s−1.[135]
The presence of impurities, Im, such as the chlorocarbons (the consequence of corrosion[181]), NO, CO
2, O
2, CO, N
2O, H
2O could have an effect on the chemical kinetics of disappearance of XeCl
* since binary collisions Im–XeCl
* possess rate constants of the order of 3×10−10 cm3s−1,[167] thus making them comparable to the XeCl
* + RCl reaction. However, given the usual impurity levels, the reaction frequencies are negligible. A practical solution has been proposed to eliminate them that involves introducing 1 torr of H
2.[181]
Process of collisional coupling between states B and C
In binary mixtures of Xe/HCl
The weak energetic gap (about 100 cm−1) between these two states (Table 2), suggests that a coupling was produced. However, this result was not exactly quantified nor was it later confirmed. No collisional coupling phenomenon induced by chlorine has been detected recently.
The role of electrons is also not well known in the coupling process. According to Finn et al.,[164] its role is negligible, although Johnson et al.[135] gave an elevated rate constant. This rate is the same, according to them, for B to C and C to B transfers. The energy difference between B and C is not zero (see Table 2). The reaction rate was estimated at 2×10−8 cm3s−1.
These couplings are demonstrated through binary collisions using an atom of xenon:
XeCl(B ; v’ = 0) + Xe → XeCl(C ; v’ = 0,1) + Xe (15) rate constant of kBC
XeCl(C ; v’ = 0, 1) + Xe → XeCl(B ; v’ = 0) + Xe (16) rate constant of kCB
The measurements of rate constants are not very consistent as can be seen in Table 28.
Table 28. Rate constants in cm3s−1 of the collisional coupling processes of states B and C. Ref kBC kCB [61] (11.0 ± 0.3) × 10−11 (7.4 ± 0.3) × 10−11 [71] 13.5 × 10−11 15 × 10−11 [16] (7.21 ± 1.97) × 10−12 (4.08 ± 1.97) × 10−12 [121] 5 × 10−11
r In experiments by Inoue et al.,[61] the vibrational levels v’=0.1 were directly excited. This is not the case in other experiments.[16][71] The last value[121] is only a theoretical estimation based on similarities with other reactions. The energetic gap ΔE = EB – EC deduced from kCB and kBC, suggests that further information could follow. Assuming that the states EB and EC were thermalized:
kBC/kCB = exp(ΔE/kT) since the statistical weights of the two states are the same.[49]
ΔE, was also inferred by Inoue et al.[61] as 85 cm−1, and as 119 cm−1 by Rives et al.,[16] while 22 cm−1 was the measurement given by Le Calvé et al.[71] (see Table 2). Only the first two values are values of ΔE which are compatible with 100 cm−1, the accepted order of magnitude. A clear difference exists between these two; an order of magnitude separates the values of kBC and kCB in the two experiments.[16][61] Grieneisen et al.[67] provided only the global rate of destruction of states B and C, in other words, quenching and coupling. For the destruction of state C, they found (15.5 ± 0.9)×10−12 cm3s−1 and for state B (10.3 ± 0.9)×10−12 cm3s−1, which are intermediate values between those of Inoue et al.[61] and Rives et al..[16] Recall that quenching by xenon only has a weak influence (Table 20). Inoue et al.[61] notably did not take account of reaction (9). If the same approach is taken for the results by Rives et al.,[16] the values of kBC and kCB are close to those of Inoue et al..[61] As was explained for kx and kH, taking account of the process (9) modifies the values of the reaction rate. On this point, Rives et al.[16] is more precise than Inoue et al..[61]
The advantage of Inoue et al.'s[61] result was in vibrational resolution, as kBC and kCB vary with the vibrational level v. For level v=70 to 130, rate constants between 15 and 20×10−11 cm3s−1 were observed.[163] kBC and kCB seems to then grow with v.
Since most of the time XeCl(B, C) is formed with a strong vibrational excitation, knowledge of the exact estimate of the variation of kBC and kCB with v; and the chemical kinetics of the vibrational relaxation and its importance relative vis-à-vis to the coupling process are important.
The role of the buffer gas
Collisional coupling is produced by binary collisions with an atom of a rare gas, Rg:
XeCl(B) + Rg → XeCl(C) + Rg (17) rate constant of kBCRg
XeCl(C) + Rg → XeCl(B) + Rg (18) rate constant of kCBRg
Dreiling and Setser[163] provide order of magnitude values for kBCRg and kCBRg for a given vibrational level. The results are shown in Table 29. This shows that the rate constants increase regularly when the vibrational level, v, of XeCl
* is higher and the rare gas, Rg, is heavier.
Table 29. Coupling rate constants in cm3s−1 by binary collisions using an atom of rare gas.[163] v He Ne Ar Kr 0–30 (0.5 to 1.8) × 10−11 (0.7 to 2.6) × 10−11 (3.0 to 11) × 10−11 (3.0 to 11) × 10−11 30–70 (1.8 to 2.5) × 10−11 (2.6 to 3.5) × 10−11 (11 to 15) × 10−11 (11.0 to 16) × 10−11 70–130 2.5 × 10−11 3.5 × 10−11 15 × 10−11 16 × 10−11
Using helium, experiments have been made at low and high pressures.[66] At high pressures, the transfer constants are of the order of (1.5 ± 0.7)×10−12 cm3s−1 and at low pressures 3.0×10−11 cm3s−1. A strong pressure induces a vibrational relaxation such that the values of v involved in the transfer are weak and vice versa for weak pressures. The only available direct determination for kBCHe gives a value less than 3×10−13 cm3s−1.[69]
For neon, the values of the rate of transfer at low and high pressure are respectively, 3.0×10−11 cm3s−1 and (0.8 ± 0.4)×10−12 cm3s−1.[66] They are inferior to those of Table 29. The direct measurement of the rate constant kBCNe gives a value less than 3.10−13 cm3s−1.[69] Finally, according to Ohwa,[156] the order of magnitude of the two rate of coupling constants would be 4.8×10−12 cm3s−1 for v=4.
For argon, the results increase. At low pressures, the order of magnitude would only be 6.0×10−11 cm3s−1.[66] Other authors[65] published rates of transfer of 1.2 ± 0.4×10−4 cm3s−1 for a pressure interval starting from 10 to 1000 torr. Direct measurements of kBCAr and kCBAr are available without specifying the vibrational levels involved:[50]
kBCAr = 36×10−4 cm3s−1 and kCBAr = 21×10−11 cm3s−1
Meanwhile, Yu et al.[69] noted a variation with temperature of kBCAr:
kBCAr = (4 ± 2)×10−12 cm3s−1 at 300K and kBCAr = (2 ± 1)×10−12 cm3s−1 at 230K.
For krypton, we can only make an estimation:
kBCKr = (4)×10−12 cm3s−1.[69]
It is clear that the collisional coupling process induced by the rare gases are not well established. Different authors give different order of magnitudes. The uncertainty on the rate constants is therefore as important as for that of xenon. The vibrational excitation seems to play a role that is still not well defined. Direct measurements for kBCRg and kCBRg are not available. From the first estimations, the phenomena seem important in the kinetics of gaseous mixtures.
Vibrational relaxation
XeCl
* is more often synthesized with strong vibrational excitation and can reach vibration quantum numbers as high as v=100.[182] This induces some vibrational relaxation that is formed by binary collision with an atom of a rare gas.[183]
Only a single measurement for xenon and level v=2 has been published.
XeCl(B; v = 2) + Xe → XeCl(B; v’ = 0.1) + Xe rate constant of kv
where kv = (2 ± 1)×10−10 cm3s−1.[61]
Most of the known results are related to buffer gases. Yet, only Dreiling and Sester[163] completed measurements. The vibrational relaxation can be written as:
XeCl
*(v) + Rg → XeCl
*(v’) + Rg (19)
The orders of magnitude of kvRg are summarized in Table 30. kvRg increases with the vibrational level of XeCl
* and heavier rare gases, Rg. Values of kvRg are assumed to be the same for states B and C.
Table 30 : Vibrational relaxation rate constants in cm3s−1 induced by binary collisions with an atom of a buffer gas, Rg.[163] v He Ne Ar Kr 0–30 (0.15 to 1.1) × 10−11 (0.5 to 2.9) × 10−11 (1.0 to 6.0) × 10−11 (0.6 to 2.7) × 10−11 30–70 (1.1 to 2.5) × 10−11 (2.9 to 6.2) × 10−11 (6.0 to 12) × 10−11 (2.7 to 5.5) × 10−11 70–130 (2.5 to 4.4) × 10−11 (6.2 to 9.5) × 10−11 (20 to 34) × 10−11 (5.5 to 7.3) × 10−11
For helium and krypton, no comparison is available.
For neon, only the reaction with first two vibrational levels of B have been documented:
XeCl(B; v = 1) + Ne → XeCl(B ; v = 0) + Ne with rate constant of kvNe=(0.3 to 0.5)×10−11 cm3s−1.[184]
For argon, the values of kvAr has been determined for v=33, 60 and 75.[90] Their values, respectively, are (17 ± 5)×10−11; (31 ± 9)×10−11 and (43 ± 10)×10−11 cm−11. Other authors placed the figure for kvAr between (10 and 15)×10−11[155] agreeing on the order of magnitude.
Disappearance pathways of the exciplex molecule
The chemical kinetics due to collisional coupling of states B and C and vibrational relaxation are not well known. The few available results often disagree, although a general idea of the situation is possible. For high vibrational levels, coupling overrides the vibrational relaxation while the contrary is true for the lowest levels,[58] even if a rare gas is involved.
The various destructive processes of XeCl(B), differ in importance. A mixture optimized for lasers is used. Neon is favored over argon because the latter strongly absorbs via the Ar+
2 ion at 308 nm.[135] Therefore, a ternary mixture (Ne/Xe/HCl) is used. The total pressure is fixed at 3 atm, the respective partial pressures is 2268.6 torr, 10 torr and 1.4 torr. The rate constants are the average values of the most reliable estimates.
The results are summarized in Table 31. For reaction (19), only the lowest vibrational levels are accounted. The lower frequency of disappearance limit is 0.40 ns−1. This process induces the highest destruction, indicating that XeCl(B) synthesized with high vibrational excitation is quickly relaxed by binary collision with neon and (probably) also by xenon. This suggests that other processes are really noticeable only after XeCl(B) is on the v=0 level, which is why reaction (17) uses the value of k BC Do relative to a low v. Once the relaxation is complete other processes take over. Depopulation by spontaneous emission is very important as well as reactions (11) and (17). These two processes lack refined measurements and determinations overall. The role of the xenon coupling is not better known but has less influence than the destruction by binary collision with HCl. Other better known processes are negligible. In particular all termolecular reactions are negligible.
Table 31 : Frequency of destruction of states B in ns−1. Processes Radiative pathway 6 7 8 9 11 12 13 15 17 19 Frequency 0.099 0.036 0.001 0.0001 0.0008 0.24 0.0006 0.0074 0.027 0.064 0.40 Percentage 11% 4% < 1% < 1% < 1% 27% < 1% 1% 3% 7% 46% Percentage after vibrational relaxation 21% 8% < 1% < 1% < 1% 50% < 1% 2% 6% 13%
The Xe
2Cl exciplex molecule
Generally, Rg2X molecules are less stable than RgX.[7] Xe
2Cl is of double interest. It can cause perturbations in laser XeCl performance because it absorbs well at 308 nm and enables the development of another type of laser based on an Xe
2Cl emission.
The Xe
2Cl molecule
Initial studies on the Xe
2Cl molecule[33][185] found:
- Its most stable configuration in the excited state has a triangular geometry C2v.[186]
- The Xe
2Cl
* excited states are complexes formed from the association of a molecular ion of Xe+
2 and an atomic ion of Cl−
. - The observed emission of the molecule is broad; the corresponding transitions result in a very repulsive ground state.
The potential curves calculated by Huestis et al.[187] from the DIM (Diatomics In Molecules) method are presented in Figure 15.
The three lowest states are covalent and repulsive. They are correlated to XeCl(X or A) and to an atom of xenon at the ground state. The experimental value of the energy at state 12Γ is 0.273 eV.[33] It is compatible with these potential curves. The following three states are ionic. The bound state 42Γ is correlated to XeCl(B) + Xe; the following, 52Γ, a repulsive state, is correlated to XeCl(C) + Xe.
Last and George[43] made a determination of the potential curves using another method, the DIIS (Diatomics In Ionic Systems) method without considering spin-orbital coupling. They found, like Huestis et al.[187] that the 42Γ state is the lowest ionic state. At the bottom of the well, this state has the configuration of an isosceles triangle, such that the distance between the equilibrium positions of Xe and Cl is 3.23 Å. According to Adams and Chabalowski[42] the Xe–Cl distance is 3.39 Å.
Initially, the potential curves of the different states were plotted by maintaining a constant and equal Xe-Xe distance at 3.25 Å (figure 16). Last and George discovered nine states (three covalent and six ionic). The potential curves of the antisymmetric states 42Γπ and 62Γπ are almost coincident with the potential curves of the symmetric states 52Γ and 62Γ. The 32Γ and 72Γ states highlighted by Huestin et al. are absent since the spin-orbital coupling were not taken into account. Inversely, three states, (22Γπ, 42Γπ and 62Γπ) with the π symmetry, were not included in their diagrams.[187]
A second study kept the separation of Xe-Cl at 3.23 Å (figure 17).
* In 42Γπ state, the molecule with isosceles triangle configuration such as the Xe-Cl and Xe-Xe distances are respectively 3.13 and 4.23 Å. The state is 0.8 eV above the 42Γ state.[43] * At the ground state, 12Γ forms a Van der Waals complex. It has a bond-dissociation energy of 0.075eV and a dissymmetric triangular configuration. The Xe–Cl distances are 3.23 and 4.06 Å and the Xe–Cl–Xe angle is 74.4°.[43] * The second excited state 22Γ is also a Van der Waals complex. It has a symmetrical geometry and an Xe–Cl distance of 3.99 Å with an Xe–Cl–Xe angle of 68.4°. Its dissociation energy is 0.055 eV.[43]
Another way of describing Xe–Cl–Xe finds the stable state to be linear and symmetric. At the ground state, the Xe-Cl distance should be 3.24 Å and the dissociation energy 0.076 eV. An excited state could exist with a geometric distance of Xe-Cl of 3.06 Å.[43] This state, which is not shown in Figures 16 and 17, would possess an energy higher than 0.72 eV to that of the 42Γ state. The bonding would be ionic.
Only an experiment conducted at the solid state[72] can be compared to these theoretical results. The special state studied was the 42Γ state. The isosceles triangle structure of this state was confirmed. Three quantities can be compared with theoretical predictions. The Xe-Xe distance is measured at 3.17 Å and that of Xe-Cl at 3 Å. The agreement in values is best for the energy at the bottom of the well that was evaluated at 3.15 eV. The fundamental vibrational frequencies for Xe–Xe, is ωx = 123 cm−1 and for Xe–Cl, ωc = 180 cm−1.
Synthetic pathways
Three principal pathways of Xe
2Cl
* synthesis are energetically possible through collisions and two others through photodissociation:
Xe*
2(A1Σ) + Cl
2 → Xe
2Cl
* + Cl (20)
Xe
* + Xe + Rg → Xe
2Cl
* + Rg (21)
Xe
2+ + Cl− + Rg → Xe
2Cl
* + Rg (22)
XeCl
*(X) + Xe + hν → Xe
2Cl
* (23)
Xe + Cl + Xe + hν → Xe
2Cl
* (24)
where Rg is a rare gas, probably xenon or a buffer gas.
The authors disagree on the relative importance of these synthetic processes. The processes depend on experimental conditions.
Through harpoon reactions
Reaction (20) is a very energetic harpoon reaction. It involves Xe*
2 excited state. According to Bruce et al.,[112] this is the dominant synthetic pathway. Other authors though do not share this view since they believe that this reaction is weak,[187] or indeed negligible.[188] Its rate constant has not yet been measured.
The photoassociative pathway
Reactions (23) and (24) were only recently discovered.[106]
The ionic pathway
According to a theoretical computation,[147] the rate of recombination α’ of the Xe+
2 and Cl−
ions when Rg = Xe (reaction (22)) was, at the first instance, estimated as 1×10–7 cm3s−1. The same authors later revised this value downward as: α’ = 5×10–8 cm3s−1.[189] This result was confirmed experimentally.[187][190] According to computations, this reaction could become important at high pressures at which Xe
2Cl
* becomes the principal reaction product, to the detriment of XeCl
* (reaction (4)).
The ternary reactions
The synthesis of Xe
2Cl
* is principally through pathway (21). According to a recent study,[62] the reaction can be interpreted as the result of two successive reactions, the second reaction corresponding to a vibrational relaxation through collision using Rg:
XeCl(B,C) + Xe ↔ Xe
2Cl
*(v)
Xe
2Cl
*(v) + Rg → Xe
2Cl
* + Rg
The starting vibrational levels of Xe
2Cl
*(v) are above the limit of dissociation of the state in XeCl
* + Xe.
In contrast, Yu et al.[69] believe that the formation of Xe
2Cl
* is through a triatomic complex, RgXeCl*, mainly :
XeCl
* + Rg → RgXeCl
* where Rg≠Xe
RgXeCl
* + Xe → Xe
2Cl
* Rg
These reactions have been observed in only argon and krypton.
The second reaction is one of displacement. Another reaction is competitive to it when xenon is replaced by krypton. This quenching process should have a rate constant higher than 1×10−13 cm3s−1.[69][177]
The lifetime of the RgXeCl
* complex is not well known. It is estimated at 200 ns for KrXeCl[69][177] and 40 ns for NeXeCl.[91] This interval in time is sufficient for the second collision to have a chance of being produced.
The rate constants have been measured as summarized in table 32. If Rg≠Xe, only two direct measurements have been carried out.[39][62] The last[191] is only an evaluation.
Table 32 : Rate constants in cm6s−1 of the reaction (21). Ref He Ne Ar Kr [39] (1.5 ± 0.5) × 10−31 [62] (3.1 ± 1.3) × 10−31 (6.0 ± 1.6) × 10−31 (9.4 ± 2.4) × 10−31 (14 ± 2) × 10−31 [191] (1.5) × 10−31
As for xenon, notice that the totality of the kDX constants of table 20 could be taken as those of the fifth column of table 32 since kDX could be merged with reaction (21).[62]
Paths of disappearance
The radiative pathway
Emission spectra
Theoretical studies[158][185] show that the allowed transitions are (figure 15) :
42Γ → 12Γ (A)
42Γ → 22Γ (B)
42Γ → 32Γ (C)
The starting states are always the same and the corresponding wavelengths, λTh, are indicated in Table 33. They can be compared to experimental values, λObs.
Table 33 : Characteristics of Xe
2Cl
* emissions.Transition Experiment:[72] λObs (nm) Theoretical estimates: λTh (nm) Theoretical estimates: relative importance Theoretical estimates: transition moment (D)[43] (A) 450 495 Dominant 2.45 (B) 490 514 Important 0.1 (C) 541 100 times weaker
Experimentally, Fajardo and Apkarian[72] observed two transitions (A) and (B) in the spectral domain, even while there was a significant wavelength shift. In most cases, a very large continuum (approximately 80 nm) was observed covering the three emissions. The maximum positioning oscillated between 450 and 500 nm. An example of this sort of spectrum is given in Figure 11. On computation, the limits of short wavelength emissions were evaluated at 443 nm.[101]
According to Last and George,[43] the Xe–Cl–Xe linear molecule ought to have produced an emission approaching the ground state at 321 nm and the transition moment should be elevated to 3.9 D. As of 2014, however, no experiment confirms this prediction.
At the solid state, the Xe
2Cl
* emission shifts towards the red range and is centered around 570 nm.[192][193] A corresponding result is observed in the liquid state.[194] This phenomenon should be owed to a distortion of the potential curves arising from molecular interactions which are closest to themselves than at the gaseous state.[citation needed] A theoretical study[195] attributes this to the polarization of the xenon matrix by Xe
2+Cl− and by Van der Waals forces.
Emission of Xe
2Cl
* trimer is only observed at high pressures of the rare gas (xenon or buffer gas) and fluorescence increases with the pressure of xenon.[33] These results follow because the synthetic pathway of Xe
2Cl
* is similar to that of reaction (21). Considering the values of the rate constant of reactions of type (21), the reaction frequency does not deviate in a significant way even when the rare gas pressure is close to 200 torr. Reaction (22) only takes place under pressure of several atmospheres.[189]
Lifetime of Xe
2Cl (42Γ)
The only state where Xe
2Cl is the original parent of a luminous emission is 42Γ). Several determinations of its lifetime obtained at the gaseous state are summarized in Table 34. The results vary and the uncertainties involved are important. The confidence interval obtained within a threshold of 5% lies between 240 and 253 ns. Of these, four values are not included.[62][80][167][190] Given the strong absolute uncertainty, another measure[111] has a common interval within the confidence interval.
Table 34 : Lifetime of Xe
2Cl(42Γ) experimentally obtained at the gaseous state, excepting for the reference given by Stevens and Krauss[158] which is a theoretical determination.Lifetime (ns) Reference 300 ± 50 [111] 185 ± 10 [67] 260 [70] 135+70−60 [39] 210 ± 25 [196] 250 ± 25 [190] 245 ± 10 [80] 328 ± 20 [197] 250 [62] 330 [158] 210 ± 20 [165] 242 ± 10 [167]
Measurements realized at the solid state provide values that are yet more dispersed such as is shown in Table 35.
Table 35 : Lifetime of Xe
2Cl(42Γ) observed at the solid state.Matrix Lifetime (ns) References Ar 460 [72] Ne 260 ± 15 [76] Kr 450 [72] Xe 663 [72] Xe 225 ± 10 [76][192]
The collision pathway
The role of chlorine donors (RCl)
Beyond the radiative disexcitation, the Xe
2Cl (42Γ) state is destroyed by a double collision with RCl. In practical terms, every author agrees that double collision is the dominant destruction pathway of Xe
2Cl when collision is involved, whatever the chlorine donor. Therefore, Xe
2Cl
* emissions are only observed at weak concentrations of RCl.[15][112][167] The values of the rate constants for reactions (24) are given in Table 36.
Xe
2Cl
* + RCl → Other products except Xe
2Cl (24)
Table 36 : Rate constants in cm3s−1 of reactions (24) for various donors of chlorine, RCl. Reference Cl
2HCl CCl
4[196] (2.2 ± 0.2) × 10−10 (4.3 ± 0.4) × 10−10 (5.4 ± 0.5) × 10−10 [70] (6.1 ± 0.2) × 10−10 [152] 2.6 × 10−10 [198] 8 × 10−10 [121] 6.1 × 10−10 [130] 6 × 10−10 [111] (3.9 ± 0.4) × 10−10 [165] (4.5 ± 0.4) × 10−10 [67] (2.6 ± 0.3) × 10−10 [80] (4 ± 1) × 10−10 [197] (7 ± 1) × 10−10 [167] (4.0 ± 1) × 10−10-10 [199] 1.8 × 10−10 [39] (6 ± 1) × 10−10
There are only two determinations for CCl
4 and these are coincident. For HCl, two values are statistically distant from others.[152][198] Giving an explanation for this distance remains difficult. The confidence interval at a threshold of 5% is from 4 to 7×10−10 cm3s−1.
In the case of chlorine, Cl
2, only one half of measurements are statistically close.[80][111][165][167] Even so, this closeness is difficult to explain. Its confidence interval at the threshold of 5% varies from 3.7 to 4.5×10−10 cm3s−1. The three chlorine donors appear to have a corresponding influence on the collisional destruction of Xe
2Cl
*.
To estimate the rate constant of the reaction:
Xe
2Cl
* + Cl → 2 Xe + 2 Cl
The value is 1×10−9 cm3s−1.[200]
The role of rare gases
These are uniquely binary reactions:
Xe
2Cl
* + Rg → Other products except Xe
2Cl (25)
The disappearance of Xe
2Cl
* by collision on a xenon atom was observed by Grieneisen et al.,[67] the reaction constant was estimated at 6×10−15 cm3s−1. However, this reaction has not been demonstrated by other authors.[39][70][165][197][199] The upper bound of the rate constant of reaction (25) is 1×10−17 cm3s−1,[197] although other authors placed this limit at 4 to 7×10−14 cm3s−1[165][199] or 5×10−13 cm3s−1.[39] The value used by Kannari et al.,[121] 8×10−12 cm3s−1, has no basis.
For ternary mixtures, the role of the buffer gas is not well known.
For argon, (3 ± 1)×10−14 cm3s−1[39] and (1.5 ± 0.4)×10−14 cm3s−1 are available.[196]
For helium, 5×10−13 cm3s−1[152] and 3×10−14 cm3s−1 are available.[119]
The role of electrons and impurities
The rate of reactions of Xe
2Cl
* + e− → 2 Xe + Cl + e− (26) does not have consistent estimates. They are summarized in Table 37.
Table 37 : Rate constants of reaction (26) in cm3s−1. Rate constants Reference 2 × 10−7 [142] 9 × 10−9 [119] 2 × 10−8 [135] 4 × 10−9 [130]
The impurities have a lesser influence in the chemical decay of Xe
2Cl than XeCl*.[167] The bimolecular rate constants of disappearance of Im
–Xe
2Cl
* are an order of magnitude lower than the relative rate constants for binary collisions ImXeCl
*. Yet, for CO
2 and nitric oxide, NO, the rate constants are of the same order of magnitude, about some 10−10 cm3s−1. Impurity levels, most often low, may influence the measurements. The reaction frequencies are negligible.
See also
References
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