# The Kinetic Study of High-Temperature Oxidation of Neopentane in a Jet-Stirred Reactor

Nurlan Amirov, Zeynep Serinyel, Guillaume Dayma, Philippe Dagaut

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Nurlan Amirov, Zeynep Serinyel, Guillaume Dayma, Philippe Dagaut. The Kinetic Study of High-Temperature Oxidation of Neopentane in a Jet-Stirred Reactor. 12th European Combustion Meeting, The Combustion Institute, Apr 2025, Edinburgh, United Kingdom. hal-05136158

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# The Kinetic Study of High-Temperature Oxidation of Neopentane in a Jet-Stirred Reactor

Nurlan Amirov<sup>a,b</sup>, Zeynep Serinyel<sup>a,b</sup>, Guillaume Dayma<sup>a,b*</sup>, Philippe Dagaut<sup>b</sup>

## Abstract

Neopentane oxidation chemistry has been subject to a particular interest as it is considered to be an ideal fuel for modeling the oxidation of alkanes due to its unique symmetrical structure. In the present study, the high-temperature oxidation of neopentane was studied in a jet-stirred reactor. The experiments for lean (φ = 0.5), stoichiometric (φ = 1.0) and rich (φ = 2.0) mixtures were carried out for residence times ranging from 0.05 to 0.24 s, at 1 atm and at two different constant temperatures of 1050 and 1100 K. Reaction intermediates and products were quantified by gas chromatography (FID/TCD). In addition, low-temperature experiments were conducted at 590–870 K at 1 atm for a residence time of 6 s and the concentrations of hydroperoxyl radical, hydrogen peroxide, water and formaldehyde were measured by cavity ring-down spectroscopy with continuous wave light (cw-CRDS). Furthermore, a recently presented kinetic mechanism in literature particularly focusing on the low-temperature oxidation of neopentane was improved. The modified mechanism agrees better with the present experimental data than the original mechanism that underpredicted neopentane reactivity at all conditions, although still further improvements are needed. Improvements were mainly achieved by modifying the rate constant of unimolecular decomposition of neopentane to tert-butyl and methyl radicals, a sensitive reaction at all conditions. The modified mechanism appears to still perform well at the low-temperature conditions. Moreover, the modifications were found having no considerable impact on simulating shock-tube ignition delay times from literature. Finally, a reaction pathway analysis was carried out to reveal the decomposition routes of the fuel.

Keywords: Neopentane; Oxidation; Jet-stirred reactor; Kinetics

<footnote><sup>a</sup> Université d'Orléans, avenue du Parc Floral, 45100 Orléans, France</footnote>

<footnote><sup>b</sup> CNRS-ICARE, 1C avenue de la Recherche Scientifique, 45071 Orléans cedex 2, France</footnote>

<footnote>* Corresponding author.</footnote>
# 1. Introduction

Neopentane, one of the representatives of the simplest branched alkanes, with its symmetrical molecular structure has been a matter of a special interest as an ideal fuel to study the oxidation kinetics of alkanes. A wide range of experimental data obtained in different set of measurements, such as jet-stirred reactor species profiles [1-3], flow reactor measurements [4], ignition delay times in shock-tubes and rapid compression machines [5], have been used in validating and improving the kinetic mechanisms [1-8].

Bugler et al. [5] evaluated ignition delay times of neopentane in shock-tube and rapid compression machine experiments at temperatures within 643 and 1718 K. The experimental data were used to validate a kinetic mechanism developed in another study by the authors [6] and satisfactory agreement was achieved over all conditions. Bourgalais et al. [2] found substantial disagreement between the experimental and predicted mole fractions of 2-methypropanal and methacrolein when testing the same kinetic mechanism against a new set of jet-stirred reactor data obtained for a lean mixture between 500-850 K. In addition, they detected formic acid in their experiments, which is formed via $\gamma$-ketohydroperoxide decomposition that was not predicted by the mechanism. These discrepancies were attributed to the absence of the Korcek reaction in the mechanism.

In another jet-stirred reactor study [3], Liu et al. detected isobutyric acid, another potential Korcek mechanism product. Hence, considering the existence of these reaction pathways, the Korcek reactions were added to the mechanism. They also considered the reaction pathways of OH radical addition to acetone and acetaldehyde. The following decomposition of acetone was found as the most dominant route for acetic acid formation. The final updated mechanism was successfully validated against a broad range of experimental data.

Apparently, the low-temperature oxidation of neopentane has been more widely studied than its high-temperature oxidation. The first study of neopentane oxidation at high temperatures was reported by Dagaut et al. [1] who carried out experiments in a jet-stirred reactor in a temperature range of 800-1230 K at 1 and 10 atm for equivalence ratios between 0.25-2. A detailed kinetic mechanism developed in the same study was found to result in a good agreement with the experimental data. Despite the initiation by this study, it has remained as the only work on the high-temperature oxidation of neopentane in a jet-stirred reactor, to the best of our knowledge. In the present study, we revisit the high-temperature oxidation regime of this fuel by means of jet-stirred reactor experiments at two constant temperatures of 1050 and 1100 K at atmospheric pressure within a residence time range of 0.05-0.24 s for three mixtures with equivalence ratios of 0.5, 1.0

and 2. Additionally, low-temperature oxidation experiments of neopentane were carried out in a jet-stirred reactor at 590-870 K for a residence time of 6 s at atmospheric pressure and the quantitative measurements of HO₂, H₂O₂, CH₂O and H₂O were performed by fast sampling and near-infrared cavity ring-down spectroscopy at low pressure. Furthermore, attempts were made to improve the kinetic mechanism recently developed by Liu et al. [3].

# 2. Experimental

A jet-stirred reactor setup, more details on which can be found in [9] was used to carry out all 75 experiments. The reactor is a fused silica sphere with a volume of 29.5 cm³ and is placed inside a stainless-steel pressure-resistant jacket. It is equipped with four nozzles of the same size of 1 mm in diameter for the injection of the inlet gases. The jets coming out of these four injectors result in stirring. The fuel and oxygen are diluted in N₂ to prevent a significant heat release. There is a mixing point at the entrance of the injectors where the fuel and oxygen meet. They flow separately until this point to prevent premature reactions. Thermal mass-flow controllers are used to measure and adjust their flow rates. The purity of the fuel used was 99.86%. Good thermal homogeneity along the entire vertical axis of the reactor (gradients < 10 K) was observed in each experiment with the help of thermocouple measurements.

The low-pressure reacting mixture samples were taken in a quartz sonic probe connected to 1-L Pyrex bulbs. The samples were subsequently analyzed by gas chromatography. Hydrocarbons were quantified by flame ionization detector on an Al₂O₃ PLOT column. The product identification was performed using an ion trap detector in electron impact mode. No specific low-temperature oxidation products were identified.

The high-temperature experiments were performed at atmospheric pressure and at constant temperatures between 1050 and 1100 K, while the residence time in the reactor was varied. The carbon balance of each sample was evaluated and determined to be within < 15%.

The quantitative measurements of HO₂, H₂O₂, CH₂O and H₂O were conducted by coupling of a jet-stirred reactor-sampling nozzle assembly and cw-CRDS. The cw-CRDS setup consists of two ultrareflective mirrors mounted 74 cm apart on a rectangular cuboid that form an optical resonator and a DFB laser emitting at about 1510 nm is employed as a continuous light source. One mirror is mounted on a ring-shaped piezoelectric transducer and the length of the cavity is adjusted over a free spectral range to ensure the frequency matching between the laser emission and a cavity mode. An avalanche photodiode is used to detect the light escaping from the cavity through the rear mirror. When the light reaches the set threshold, the laser beam is switched off by a fibered acousto-optic modulator. The light intensity is
1 recorded and the ring down time is determined, which
2 is further converted to the concentrations of the
3 absorbing species. More details on this experimental
4 set up have been presented by Djehiche et al. [10].

### 3. Kinetic Modeling

8 The kinetic mechanism presented by Bugler et al.
9 [6] was updated in a recent study by Liu et al. [3],
10 however as the updates mostly focused on the low-
11 temperature oxidation chemistry of neopentane, the
12 mechanism still remains insufficient in predicting the
13 high-temperature behavior of neopentane oxidation.
14 In this regard, attempts were made to further improve
15 the mechanism with a focus on the high-temperature
16 sub-mechanism of neopentane. The complete set of
17 modifications is presented in Table 1, including the
18 reactions and the final corresponding rate parameters.
19 The Perfectly Stirred Reactor (PSR) module in
20 CHEMKIN-PRO 2024 R2 [11] was used to perform
21 all simulations.

22 The improvements were mainly achieved by
23 modifying the rate constant of unimolecular
24 decomposition of neopentane to tert-butyl and methyl

<caption>50 Table 1</caption>

51 Modified reactions and the new rate parameters.

<table><thead><tr><th>Reaction</th><th>A</th><th>n</th><th>E</th><th>Ref.</th></tr></thead><tbody><tr><td>neo-C<sub>5</sub>H<sub>12</sub> = TC<sub>4</sub>H<sub>9</sub> + CH<sub>3</sub></td><td>8.66E+12</td><td>0.000</td><td>60426.61</td><td>[12-13]</td></tr><tr><td>neo-C<sub>5</sub>H<sub>12</sub> = IC<sub>4</sub>H<sub>8</sub> + CH<sub>4</sub></td><td>2.30E+12</td><td>0.000</td><td>60441.70</td><td>[12-13]</td></tr><tr><td>neo-C<sub>5</sub>H<sub>12</sub> + OH = NEOC<sub>5</sub>H<sub>11</sub> + H<sub>2</sub>O</td><td>6.00E+07</td><td>+1.763</td><td>743.20</td><td>[3]</td></tr><tr><td>IC<sub>4</sub>H<sub>8</sub> + OH = IC<sub>4</sub>H<sub>7</sub>+H<sub>2</sub>O</td><td>1.50E+08</td><td>+1.530</td><td>775.00</td><td>[14]</td></tr><tr><td>CH<sub>3</sub> + HO<sub>2</sub> = CH<sub>4</sub>+O<sub>2</sub></td><td>1.00E+12</td><td>0.000</td><td>0.00</td><td>[15]</td></tr><tr><td>CH<sub>3</sub> + CH<sub>3</sub> (+M) = C<sub>2</sub>H<sub>6</sub> (+M)</td><td>2.12E+16</td><td>-0.970</td><td>620.00</td><td>[15]</td></tr></tbody></table>

### 4. Results and Discussion

#### 4.1 Experimental and modeling results

58 The experimental and simulated mole fractions of
59 the fuel and various detected species at different high-
60 temperature conditions as a function of residence time
61 are provided in Fig. 1–6. The quantified hydrocarbons
62 include, methane, ethane, ethylene, acetylene,
63 propene, propyne, allene, 1,3-butadiene, 1-butene,
64 isobutene, and neopentane. The experimental mole
65 fraction data is presented with a 15% uncertainty bar.

66 The results of the predictions of the mole fractions
67 by the original and the modified Liu mechanism are
68 also compared in the same figures. Generally, the
69 modified mechanism performs better than the original
70 one that is underpredicting the reactivity of the fuel at
71 all conditions. The simulated results at 1050 K for all
72 three equivalence ratios (Fig. 1–3) agree better with
73 the experimental results, except for some
74 discrepancies for C<sub>3</sub>H<sub>4</sub>-A, C<sub>4</sub>H<sub>8</sub>-1 and C<sub>2</sub>H<sub>2</sub> mole
75 fractions, particularly at lean condition. The
76 neopentane reactivity is slightly underpredicted at
77 1100 K (Fig. 4-6), as well as the mole fractions of
78 some species, such as C<sub>3</sub>H<sub>4</sub>-A, C<sub>2</sub>H<sub>4</sub>, C<sub>3</sub>H<sub>6</sub>, C<sub>4</sub>H<sub>8</sub>-1.

25 radicals, a sensitive reaction at all conditions. The rate
26 constant calculated by Sivaramakrishnan et al. [12]
27 and used by Zhang et al. [13] in a recent pyrolysis
28 mechanism is faster than that adopted in the initial Liu
29 mechanism, ultimately contributing to its prediction
30 capability. Sivaramakrishnan et al. [12] determined
31 the rate parameters for this reaction based on the
32 studies of neopentane decomposition at high
33 temperatures (1260–1566 K) in shock tube
34 experiments and by ab initio transition state theory-
35 based master equation theoretical analysis. It was
36 proposed that the departed CH<sub>3</sub> radical can roam
37 around the tert-butyl radical and abstract an H-atom
38 leading to the formation of CH<sub>4</sub> and isobutene.
39 Although the C–C bond scission to tert-butyl was
40 determined as the major decomposition pathway, the
41 roaming reaction was also found to have a significant
42 role in neopentane decomposition. It was found that
43 the branching ratio of the roaming reaction decreases
44 with increasing temperature having values between 0
45 and 1 from high to low temperatures. For the studied
46 conditions, the roaming fraction was reported to be
47 0.21 ± 0.05. Hence, the roaming reaction is also added
48 to the updated kinetic mechanism in this study.

79 The predictions are better at higher equivalence ratios.

80 At φ = 0.5 at this temperature, the original mechanism
81 fails in predicting the point where the mole fractions
82 of some species fall dramatically, which is between
83 the residence times of 0.14 and 0.16 s experimentally.

84 The updated mechanism perfectly simulates this drop
85 in mole fractions at the exact point, but still
86 underpredicts the mole fractions of some species,
87 especially after this point.

88 Fig. 7. shows the mole fraction profiles of HO<sub>2</sub>,
89 H<sub>2</sub>O<sub>2</sub>, CH<sub>2</sub>O and H<sub>2</sub>O measured at low temperatures.
90 In general, it can be stated that the mechanism
91 compared to its original version still maintains its
92 performance well at low-temperature conditions after
93 specific modifications for improving its predictive
94 capability at high temperatures. However, there are
95 still discrepancies in the predictions of both
96 mechanisms, both of which overpredict HO<sub>2</sub> and
97 H<sub>2</sub>O<sub>2</sub> mole fractions, while underpredict CH<sub>2</sub>O mole
98 fractions. The updated mechanism performs even
99 better than the original mechanism in predicting H<sub>2</sub>O<sub>2</sub>
100 mole fractions. Unlike the other three species, the
101 simulated mole fractions of water by both
102 mechanisms are in good agreement with the
103 experimental measurements.
<figure><img src="image_1.png" /><figcaption>Fig. 1. Mole fraction profiles at $\varphi = 0.5$, $X_{0,fuel} = 0.2\%$, $T = 1050$ K, $p = 1$ atm. Symbols – experimental data, lines – simulations (dashed – original mechanism, solid – modified mechanism).</figcaption></figure>

<figure><img src="image_2.png" /><figcaption>Fig. 2. Mole fraction profiles at $\varphi = 1.0$, $X_{0,fuel} = 0.2\%$, $T = 1050$ K, $p = 1$ atm. Symbols – experimental data, lines – simulations (dashed – original mechanism, solid – modified mechanism).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 3. Mole fraction profiles at $\varphi = 2.0$, $X_{0,fuel} = 0.2\%$, $T = 1050$ K, $p = 1$ atm. Symbols – experimental data, lines – simulations (dashed – original mechanism, solid – modified mechanism).</figcaption></figure>

The mechanism was further validated against ignition delay time data from literature obtained in different shock-tube studies performed at pressures ranging from 0.78 to 26 atm and at temperatures ranging from 786 to 1718 K [5]. The results of all simulations revealed that the simulated ignition delay times by both the original and the adjusted mechanism are in good agreement with the experimental measurements and the modifications has no

17 significant impact on the performance of the 18 mechanism.

Fig. 8. shows the results of the sensitivity analysis carried out for neopentane in a stoichiometric mixture at a constant residence time of 0.1s for two different temperatures. The unimolecular decomposition of neopentane to tert-butyl and methyl radicals was found to be the most negatively sensitive reaction with extremely higher sensitivity coefficients compared to all other top sensitive reactions. Therefore, the
<figure><img src="image_4.png" /><figcaption>Fig. 4. Mole fraction profiles at φ = 0.5, X<sub>0,fuel</sub> = 0.2 %, T = 1100 K, p = 1 atm. Symbols – experimental data, lines – simulations (dashed – original mechanism, solid – modified mechanism).</figcaption></figure>

1

2

<figure><img src="image_5.png" /><figcaption>Fig. 5. Mole fraction profiles at φ = 1.0, X<sub>0,fuel</sub> = 0.2 %, T = 1100 K, p = 1 atm. Symbols – experimental data, lines – simulations (dashed – original mechanism, solid – modified mechanism).</figcaption></figure>

3

4

<figure><img src="image_6.png" /><figcaption>Fig. 6. Mole fraction profiles at φ = 2.0, X<sub>0,fuel</sub> = 0.2 %, T = 1100 K, p = 1 atm. Symbols – experimental data, lines – simulations (dashed – original mechanism, solid – modified mechanism).</figcaption></figure>

5

6

7

8 sensitivity coefficients of this reaction were divided by three in Fig. 8. to have a better view of the sensitivity of the remaining reactions. All negatively sensitive reactions appear to get more dominant as the temperature increases. This increase in the sensitivity is more pronounced for neo-C<sub>5</sub>H<sub>12</sub> ⇌ TC<sub>4</sub>H<sub>9</sub> + CH<sub>3</sub> from 1050 to 1100 K. The other negatively sensitive reactions include the newly added reaction neo-C<sub>5</sub>H<sub>12</sub> ⇌ IC<sub>4</sub>H<sub>8</sub> + CH<sub>4</sub> and neo-C<sub>5</sub>H<sub>12</sub> + OH ⇌ neo-C<sub>5</sub>H<sub>12</sub> + H<sub>2</sub>O, the rate parameters of which have been

18 modified. The positively sensitive reactions also tend to be more sensitive at higher temperature. IC<sub>4</sub>H<sub>8</sub> + OH ⇌ IC<sub>4</sub>H<sub>7</sub> + H<sub>2</sub>O, CH<sub>3</sub> + HO<sub>2</sub> ⇌ CH<sub>4</sub> + O<sub>2</sub> and 2CH<sub>3</sub> (+M) ⇌ C<sub>2</sub>H<sub>6</sub> (+M) are among the top positively sensitive reactions, for which the rate constants were changed in the updated mechanism.

24

## 4.2 Reaction pathway analysis

26

27 The decomposition routes of neopentane were
<figure><img src="image_7.png" /><figcaption>1 Fig. 7. Mole fraction profiles of hydroperoxyl radical, 2 hydrogen peroxide, formaldehyde and water at φ = 1.0, X₀,fuel 3 = 2%, τ = 6 s, p = 1 atm. Symbols – experimental data, lines 4 – simulations (dashed – original mechanism, solid – 5 modified mechanism).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>6 Fig. 8. Sensitivity analysis on neopentane carried out at T = 7 1050 and 1100 K using the modified mechanism, φ = 1.0, 8 X₀,fuel = 0.2 %, τ = 0.1 s, p = 1 atm.</figcaption></figure>

9
10 studied via reaction pathway analysis carried out for
11 the stoichiometric condition at two different
12 temperatures and at the residence time of 0.1 s (Fig.
13 9.). The modified mechanism was used to perform the
14 analysis, which at this residence time well predicts the
15 neopentane mole fraction at 1050 K, while slightly
16 overpredicts it at 1100 K. The consumption of
17 neopentane takes place via three routes, among which
18 its thermal decomposition to tert-butyl and methyl
19 radicals plays more role at 1100 K, while its H-
20 abstraction to neopentyl radical is more responsible
21 for its consumption at 1050 K. Both reactions account
22 for 44 % of the fuel decomposition at 1100 K. In
23 contrast to previous findings [1], apparently
24 metathesis reactions become less dominant at higher

temperatures. Due to its symmetric structure, only a
single radical, neopentyl, forms via the H-abstraction
reactions of neopentane, particularly by the attack of
H and OH radicals. The roaming reaction forming
isobutene and methane does not have a crucial role in
the fuel consumption but still constitutes about 10 %
of the flux. Although the consumption of neopentane
does not considerably contribute to the formation of
isobutene directly, both intermediates, tert-butyl and
neopentyl radicals further decompose to isobutene.
The neopentyl radical totally decomposes to isobutene
by a C–C bond scission reaction regardless of
temperature. While 80 % of tert-butyl radical forms
isobutene at 1050 K, this increases with temperature
up to 87 % at 1000 K. Interestingly, a low-temperature
behavior of neopentane oxidation is still observed at
1050 K as 16 % of the consumption of tert-butyl
corresponds to its addition to molecular oxygen
leading to the formation of tert-butylperoxy radical.
As expected, it gets less important at higher
temperature. Additionally, only a meager 4 % of tert-
butyl decomposition forms propene. Hence, isobutene
is the main product formed from the decomposition of
neopentane at all conditions.
Isobutene mostly forms, via H-abstraction
reactions, the resonantly stabilized isobutenyl radical.
While this route is responsible for 74 % of its
consumption at 1050 K it increases to 77 % at 1100
K. Moreover, vinylic radical forms by H-abstraction
reaction only via OH radical attack. Accounting for 7
% of the flux at 1050 K, its formation from isobutene
does not appear to be important at 1100 K. Isobutenyl
radical reacts with CH₃ to form 2-methyl-1-butene
that corresponds to 49 – 32 % of the flux from low to
high temperature. On the other hand, β-scission of the
radical to allene takes the main role in its consumption
at high temperature as it constitutes 54 % of the flux
at 1100 K. One more low-temperature reaction is
predicted by the mechanism to occur at the
investigated conditions, the formation of 2-
methylallylperoxy radical. As expected, this reaction
also becomes less important at 1100 K. 2-methyl-1-
butene reacts with H radicals to form back isobutene
and CH₃ that is responsible for around 57 % of its
consumption flux.
57 to 66 % of allene isomerizes to propyne from
low to high temperature. Both allene and propyne
consume to propargyl radicals by H-abstraction
reactions that become a little more dominating for
their decomposition at higher temperature. Propargyl
radicals almost totally consume by reacting with
molecular oxygen to form ketene and formyl radical
at both temperatures. The major reaction responsible
for propyne consumption appears to be its CH₃
elimination to acetylene regardless of temperature.
Acetylene in turn mostly forms ketenyl radical
(HCCO) constituting 50–67 % of its consumption flux
from 1050 to 1100 K. It also forms C₂H₃ radicals,
considerably at 1050 K, via H addition reaction,
which is of much lesser importance at higher
temperature.
<figure><img src="image_9.png" /><figcaption>1. Fig. 9. Reaction pathway analysis for neopentane oxidation at T = 1050 and 1100 K performed using the modified mechanism, φ = 1.0, X<sub>o,fuel</sub> = 0.2%, τ = 0.1 s, p = 1 atm.</figcaption></figure>

5. Conclusion

The high-temperature oxidation of neopentane was investigated in a jet-stirred reactor for lean, stoichiometric and rich mixtures at 1 atm. The experiments were carried out at two different constant temperatures (1050 and 1100 K) for residence times in the range of 0.05-0.24 s. A recently published low-temperature focused neopentane kinetic mechanism was tested against the present experimental data, as a result of which a strong disagreement was found. The mechanism was updated in a few steps, based on the results of sensitivity analysis, that found to perform better than the original mechanism at all conditions. The major role in achieving the better agreements is played by the updated rate parameters of the unimolecular decomposition of neopentane to tert-butyl and methyl radicals, as well as by the newly added roaming reaction of neopentane directly

forming isobutene and methane. Despite the improvements, the mechanism still does not predict the mole fraction profiles of some species at certain conditions. In general, the predictive performance of the updated mechanism gets better with decreasing temperature and with increasing equivalence ratio in the given experimental range of conditions. The simulated mole fractions of certain species by the mechanism for the low-temperature oxidation of neopentane was not found to change considerably after the modifications. Furthermore, the modifications were determined to have no substantial effect on the predictive performance of the mechanism when validated against ignition delay times reported in literature.

Reaction pathway analysis carried out at two temperatures at the residence time of 0.1 s revealed that neopentane yields tert-butyl and neopentyl radicals, both of which ultimately lead to the
1 formation of isobutene. Although not of a major

2 importance, the roaming reaction of neopentane

3 forming isobutene still has an effect on the
4 decomposition of neopentane.

5 Taking into account that the mole fraction profiles

6 of some species at the studied range of experimental

7 conditions are still not well predicted by the modified

8 mechanism, further improvements are necessary for

9 eliminating the prediction failures and to achieve an

10 enhanced agreement with wide range of experimental

11 data.

12

## Declaration of competing interest

14

15 The authors declare that they have no known

16 competing financial interests or personal relationships

17 that could have appeared to influence the work

18 reported in this paper.

19

## Acknowledgements

21

22 Support from the CAPRYSSES project (ANR-11-

23 LABX-006-01) funded by ANR through the PIA

24 (Programme d'Investissement d'Avenir) is gratefully

25 acknowledged. We thank Dr. M. Djehiche for his help

26 with CRDS measurements.

27

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