High-Temperature Rate Constants for the Reaction of Hydrogen

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A: Kinetics, Dynamics, Photochemistry, and Excited States

High-Temperature Rate Constants for the Reaction of H Atoms with Tetramethoxy-Silane and Reactivity Analogies between Silanes and Oxygenated Hydrocarbons Sebastian Peukert, Pavel Yatsenko, Mustapha Fikri, and Christof Schulz J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03160 • Publication Date (Web): 30 May 2018 Downloaded from http://pubs.acs.org on May 30, 2018

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The Journal of Physical Chemistry

High-Temperature Rate Constants for the Reaction of H Atoms with Tetramethoxy-Silane and Reactivity Analogies between Silanes and Oxygenated Hydrocarbons

Sebastian Peukert1*, Pavel Yatsenko2, Mustapha Fikri1, Christof Schulz1

1

IVG, Institute for Combustion and Gas Dynamics – Reactive Fluids and CENIDE, Center for Nanointegration Duisburg-Essen, University of Duisburg-Essen, 47048 Duisburg, Germany

2

Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia

Corresponding Author: Sebastian Peukert IVG, Institute for Combustion and Gas Dynamics – Reactive Fluids University of Duisburg-Essen 47048 Duisburg, Germany Phone: +49 202 3793511 Email: [email protected]

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Abstract The shock-tube technique has been used to investigate the H-abstraction reaction H + Si(OCH3)4 → H2 + Si(OCH2)(OCH3)3 behind reflected shock waves. C2H5I was used as a thermal in situ source for H atoms. The experiments covered a temperature range of 1111–1238 K, and pressures of 1.3–1.4 bar. H-atom concentrations were monitored with Atomic Resonance Absorption Spectrometry (ARAS). Fits to the temporal H-atom concentration profiles based on a developed chemical kinetics reaction mechanism were used for determining bimolecular rate constants. Experimental total H-abstraction rate constants were well represented by the Arrhenius equation ktotal(T) = 10−9.16±0.24 exp(–25.5±5.6 kJ mol−1/RT) cm3s−1. Transition state theory (TST) calculations based on the G4 level of theory show excellent agreement with experimentally obtained rate constants, i.e., the theory values of k(T) deviate by less than 25% from the experimental results. Regarding H abstractions, we have compared the reactivity of CH bonds in Si(OCH3)4 with the reactivity of C-H bonds in dimethyl ether (CH3OCH3). Present experimental and theoretical results indicate that at high temperatures, i.e., T > 500 K, CH3OCH3 is a good reactivity analog to Si(OCH3)4, i.e., kH+Si(OCH3)4(T)~1.5×kH+CH3OCH3(T). Based on these results, we discuss the possibility of drawing reactivity analogies between oxygenated silanes and oxygenated hydrocarbons.

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1. Introduction Silicon organic molecules are used as precursor compounds for the synthesis of siliconcontaining nanoparticles and coatings, which have a broad spectrum of potential applications. As an anode material, silicon nanoparticles can increase the capacity of lithium-ion batteries1-2, they can be used to partially replace rare earth elements as active material in thermoelectric generators3, and by connecting them with fluorescence markers they can be also used as biocompatible materials in medical diagnostics4. If ongoing chemical processes during the thermal decomposition and combustion of precursor species in, e.g., microwave reactors3 or wall-heated reactors5 is qualitatively and quantitatively understood, chemical kinetics modeling can be a powerful approach to rationalize and optimize the nanoparticle synthesis. However, often the chemical processes taking place during the precursor decomposition are not well understood and often simplified by gross reactions. At conditions relevant for practical combustion-based synthesis processes, in particular at high temperatures, no or only limited rate constant data are available for many potentially important reactions. Therefore, analog to modeling the combustion of hydrocarbon fuels, modeling gas-phase material synthesis requires the development of chemical kinetics models based on detailed experimental data and theoretical understanding. In complex mechanisms, reactions are classified in different groups like eliminations, isomerisations, H abstractions, etc. In flames, the initial fuel decomposition pathways are dominated by H-abstraction-reactions6. Besides the combustion chemistry of hydrocarbons, laminar premixed flat flames of H2/O2 stabilized on model burners have been proven to be also valuable tools for studying the chemical processes during nanoparticle precursor reactions7. In H2/O2-flames, doped with a precursor compound, H and OH are primary chain carriers. Therefore, H abstraction by H and OH are key reactions under these oxidative conditions. In complex chemical mechanisms used for combustion modeling, kinetics data of reaction classes like H abstractions can be quantitatively described in terms of structure–activity relationships (SAR). One possibility to establish SAR is to correlate energetic barrier heights with bond dissociation energies (BDE). This was also shown in a recent H-ARAS (Atomic Resonance

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Absorption Spectrometry) shock-tube study from our laboratory, where we have investigated the reactions H + SiH4 → H2 + SiH3 and H + Si(CH3)4 → H2 + Si(CH2)(CH3)3 (SiH4: Monosilane; Si(CH3)4: tetramethyl-silane)8. It was found that Si(CH3)4 and neo-pentane (C(CH3)4), which is the analog hydrocarbon to Si(CH3)4, have similar reactivity towards H abstractions. On the other hand, SiH4 and the analog hydrocarbon CH4 have completely different reactivity towards H abstractions. In case of Si(CH3)4 and C(CH3)4, the C-H bonds in both compounds have quite similar BDE. They differ by approximately 4 kJ/mol, whereas in case of SiH4 and CH4 the BDE between the Si-H and C-H bond are markedly different (∆H298 = 383.7 kJ/mol for Si-H and 439.3 kJ/mol for C-H)9. This result is interesting in terms of possible reactivity analogies between silicon-organic molecules and corresponding hydrocarbons. For hydrocarbons, detailed SAR for H abstractions have been developed based on elementary kinetics studies and high-level electronic structure theory10-14. Reactivity analogies between silicon-organic species and analog hydrocarbons would strongly facilitate chemical kinetics modeling of high-temperature processes taking place in reactor systems applied for the nanoparticle and thin-film synthesis. We have now studied decomposition reactions of tetramethoxy-silane (TMOS; Si(OCH3)4), which is frequently used as a precursor for SiO2 coatings and particles15-16. Since it is the simplest homolog in the group of alkoxy-silanes, Si(OR)4, it is also an ideal model compound for an oxygenated silicon organic precursor molecule. The structure of Si(OCH3)4 obtained from a geometry optimization is presented in Fig. 1.

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Fig. 1. Geometry optimized structures of Si(OCH3)4 (left) and CH3OCH3 (right) at the B3LYP/6-31-g(2df,p) level of theory.

In terms of reactivity per C-H bond, dimethyl ether (CH3OCH3) is proposed to be a suitable reactivity analogy. In both molecules, CH3 groups are bonded to an O atom and appearing C-H bonds have similar BDE. In this work, electronic energies of species like Si(OCH3)4 and CH3OCH3 were calculated with the G4 composite method17. In order to convert the electronic energies to thermodynamic properties, the atomization method was employed for calculating enthalpies of formation and hence also BDE18. The G4-method is used since we suppose that its application yields reasonable thermochemical data for silanes. These examples are used to support this assumption: For the silanes Si(CH3)4, Si2H6, and Si3H8, following experimentally based standard enthalpies of formation, ∆Hf°, were reported: -233.2 kJ/mol19, 71.6 kJ/mol20, and 108.4 kJ/mol21. Corresponding ∆Hf° values, obtained from G4-calculations using the atomization method, are: 237.9 kJ/mol, 70.6 kJ/mol, and 106.1 kJ/mol. Deviations to experimental data are below 5 kJ/mol. Regarding Si(OCH3)4, there are two literature values for ∆Hf°, which are both based on calorimetric measurements: -1180.0 kJ/mol22 and -1225.9 kJ/mol23. The present G4-calculation yields ∆Hf° = -1209.7 kJ/mol, which is in between these two experimental numbers. Considering the uncertainties and comparing these results suggests that the G4-method can be also applied for obtaining reasonable thermochemical data of Si-O-C containing compounds. For Si(OCH3)4, the calculated average BDE for a C-H bond is 394.4 kJ/mol and for CH3OCH3, it is 398.5 kJ/mol. This difference is well within the uncertainty of the G4 method. Based on these arguments, we try to verify if CH3OCH3 is an appropriate reactivity analog to Si(OCH3)4 with respect to H abstractions. Therefore, high-temperature rate constants were determined for reaction (R1).

H + Si(OCH3)4 → H2 + Si(OCH2)(OCH3)3

(R1)

Experimental rate constants were compared to ab initio-based transition state theory (TST) predictions. Both, experimental and theoretical rate constants for (R1), k1, were then compared to available rate constant data for the H abstraction (R2).

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H + CH3OCH3 → H2 + CH2OCH3

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(R2)

To the best of our knowledge, this is the first study providing direct high-temperature rate constant data k1 and which discusses possible implications in terms of reactivity analogies.

2. Experiment and theory 2.1 Shock-tube facility and H-ARAS technique All experiments were performed in a stainless-steel diaphragm-type shock tube. Driver and driven section have a length of 3.0 and 5.5 m, respectively, and an inner diameter of 80 mm. Aluminum sheets with 50 µm thickness were used as diaphragm between driver and driven sections. The driver section was evacuated down to 3×10–3 mbar and between experiments and the driven section was routinely pumped down to pressures of 1.0×10–6 mbar. To generate a shock wave, helium (Air Liquide, 99.999%) is filled into the driver section until the diaphragm bursts. The driven gas in the low-pressure part was argon of high purity (Air Liquide, 99.9999%) with small quantities of Si(OCH3)4 (7.9–8.8 ppm) and C2H5I ( ∼0.4 ppm). The purities of the chemicals used were: Si(OCH3)4 (Sigma Aldrich, ≥99%); C2H5I (Sigma Aldrich, ∼98%); N2O (Air Liquide; ≥99.999%), H2 (Air Liquide, 99.9999%). All gas mixtures were prepared in a 50-l stainless-steel mixing vessel based on the partial pressure method and allowed to homogenize for two hours before use. The calculations necessary for determining the post-shock conditions are based on 1D gas-dynamic equations and require the pre-shock conditions (T and p) as well as the incident shock-wave velocities as input parameters. The velocity of the incident shock wave was measured by four pressure transducers (PCB model 112A21) that were mounted at equal distances of 150 mm on the top of the driven section. One additional pressure transducer (Kistler 603A) was installed 20 mm upstream of the end wall to measure the arrival times of the reflected shock waves. Two LiF

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windows transparent in the vacuum ultraviolet (VUV) were installed 20 mm upstream of the end wall of the driven section at opposite sides as optical access for absorption measurements. Behind the reflected shock waves, the reaction progress was monitored by time-resolved H- ARAS at the Lyman-α line (121.6 nm). The Lyman-α radiation is produced in a microwavedischarge lamp consisting of a microwave generator, a microwave antenna, and a quartz tube. The antenna is mounted around a quartz tube and connected to the microwave generator (Sairem, 2.45 GHz, 200 W). By using a 5 dB damping resistor, the power is reduced to 60 W. A gas mixture containing 1% H2 in He is flown through the quartz tube and adjusted to a pressure of 7 mbar. One end of the quartz tube is connected to the optical port of the shock tube, and the generated VUV radiation was transmitted across the shock tube through the VUV-LiF windows and collected by a solar-blind photomultiplier (Hamamatsu/R8487). The photomultiplier is located in a metal housing that is purged by O2 that acts as a spectral filter that isolates the Lyman-α radiation and hence achieves the required spectral resolution according to the concept introduced by Appel and Appleton24. At atmospheric pressure the O2 VUV spectrum provides a narrow region of high transmission at 121.6 nm, which is suited to isolate the Lyman-α line while suppressing neighboring lines. Signals of the photomultiplier as well as the PCB and Kistler pressure transducers are recorded by two oscilloscopes (PicoScope 5442A). The experimental observation period was 1000 µs. The oscilloscopes are triggered by a pulse derived from the first pressure transducer on top of the driven section of the shock tube. For the purpose of chemical kinetics modeling, the measured absorption–time profiles need to be converted into absolute H-atom concentration–time profiles. Within the VUV lamp, selfabsorption at the resonance frequency occurs causing a self-reversal of the emission profile. Moreover, the emission line is broader then the absorption line of the detected H-atoms. Therefore, the Lambert-Beer law is not directly applicable for interpreting the measured absorption. Therefore, calibration experiments were performed under experimental conditions that provide a wide range of well-known H-atom concentrations. The well-established reaction sequence starting with N2O (+M) → N2 + O (+M), followed by H2 + O → OH + H and OH + H2 → H2O + H was applied for the controlled generation of H atoms, with known concentrations of N2O and H2 diluted in Ar25. This procedure is suitable because the thermal decomposition of H2 7



is very slow at temperatures below 2000 K. Below 2000 K, a quasi-stationary concentration profile of H atoms cannot be achieved within the observation period of 1 ms and the dynamic increase of the observed absorption is used to correlate it with the respective H-atom concentration25. The functional relationship between absorber concentration and absorption A can be fitted to a modified Lambert-Beer equation, A = 1 – exp(-l σ [H]n), where A is the measured absorption, l the absorption path length in cm, [H] is the concentration of the absorber (H atoms) in cm–3, and σ and n are fit parameters providing the correlation [H] = f(A). In the present work we found σ = (3.74±0.12)×10−9 cm0.818 and n = 0.606±0.001. Within the investigated temperature range, no temperature dependence of the calibration was found. For modeling of the experimentally obtained [H]t profiles, the program Chemical Workbench (Version 4.1.15340) was used26.

2.2 Theory To rationalize the findings reported in this work, the experimental data were supported by TST calculations. Since the G4 composite approach has been previously used for calculations of energy profiles of chemical processes8,27-29, TST calculations were based on molecular properties and energetics at the G4 level of theory. The rate constants for H abstractions were calculated using TST, as implemented in the KiSThelP code30. The one-dimensional asymmetric Eckart correction was applied to account for tunneling. The G4 method is another composite method in which a sequence of ab initio calculations is performed to determine the total energy of a molecular compound17. This method calculates geometries and frequencies using B3LYP density functional theory with the 6-31G (2df,p) basis set. The frequencies are scaled by a factor of 0.9854 prior to their use to calculate zero-point energies (ZPE). The electronic structure calculations were performed using the Gaussian09 program package31. TST calculations were carried out using the ab initio-based rovibrational properties and energetics of the minima and transition states to obtain theoretical rate constants.

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Internal rotations around the bonds of the CH3 groups attached to the O atoms were treated as hindered rotations by using the hindered-rotor density-of-states method32, which is implemented in the KiSThelP program. In the Si(OCH3)4 molecule and in the transition state structure for H abstractions, four vibrational modes have been treated as hindered rotors. Rotational barrier heights for the CH3 rotors (around 2.1 kJ/mol) have been obtained from relaxed potential energy surface (PES) scans with dihedral angles used as coordinates for the scans. However, for reaction R1, TST calculations considering hindered rotors do not make a difference to the rigid-rotor harmonic-oscillator (RRHO) approximation because in case of Si(OCH3)4, the partition functions of the reactant and the transition state basically cancel out.

3. Results and Discussion In all experiments, C2H5I was used as a source of H atoms. The dissociation of C2H5I is a wellcharacterized two-channel process33-36. C2H5I → C2H4 + H + I

(R3a)

C2H5I → C2H4 + HI

(R3b)

The primary products of the C-I bond fission are C2H5 and I atoms. Since C2H5 radicals rapidly decompose under the conditions of the present experiments, the products of the C-I bond fission are C2H4, I, and H (R3a). Fig. 2 shows an example of measured H-atom concentration– time profile derived from a C2H5I experiment.

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Fig. 2. Thermal decomposition of C2H5I: Comparison between measured and calculated H-atom concentration profile. Experiment at T = 1134 K, p = 1.36 bar; x(C2H5I)0 = 0.31 ppm; simulation with k3a and k3b from Bentz et al.34.

For modeling measured [H]t profiles, it is necessary to derive a reaction mechanism. The mechanism employed in this work is presented in Table 1.

Table 1. Reactions used to simulate [H]t from H + Si(OCH3)4. Reaction C2H5I C2H4 + I + H

Rate constant

C2H5I

k(T) = 1.7×1013 exp(−26680 K/T) s–1

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k(T) = 7.0×10 exp(−22810 K/T) s

C2H4 + HI

13

–1

Reference [34] [34]

–1

[37]

Si(OCH3)4

CH3 + OSi(OCH3)3

k(T) = 4.1×10 exp(−36324 K/T) s

Si(OCH3)4

CH3OH + CH2OSi(OCH3)2

k(T) = 1.3×1011 exp(−26221 K/T) s–1

[37]

k(T) = 3.8×1014 exp(−30190 K/T) s–1

[38]

See text

This work

CH2OSi(OCH3)3

CH2O + Si(OCH3)3

H + Si(OCH3)4

H2 + Si(OCH2)(OCH3)3

OH + Si(OCH3)4

H2O + CH2OSi(OCH3)3

k(T) = 2.7×10−11 exp(−397 K/T) cm3s–1

[38]

CH3 + Si(OCH3)4

CH4 + CH2OSi(OCH3)3

k(T) = 1.7×10−12 exp(−5032 K/T) cm3s–1

[38]

H + CH2OSi(OCH3)3

Si(OCH3)4

k(T) = 1.2×10−10 cm3s–1

[38]

H + CH2OSi(OCH3)2

Si(OCH3)3

k(T) = 1.2×10−10 cm3s–1

[38]

k(T) = 1.0×1013 exp(−10065 K/T) s–1

[38]

C2H5OSiO(OCH3) = C2H4 + CH3OH + SiO2

k(T) = 5.0×1013 exp(−30195 K/T) s–1

[38]

H + CH2OSiO(OCH3)

k(T) = 1.2×10−10 cm3s–1

[38]

k(T) = 1.7×10−11 cm3s–1

[38]

CH2OSi(OCH3)2

H + Si(OCH3)3

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C2H5OSiO(OCH3) OSi(OCH3)2

HSi(OCH3)3


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k(T) = 2.2×10−16 T1.6 exp(−1057 K/T) cm3s–1

[38]

k(T) = 1.0×1014 exp(−27183 K/T) s–1

[38]

k(T) = 1.0×1013 exp(−12629 K/T) s–1

[38]

CH2O +CH3 + SiO2

k(T) = 5.0×1013 exp(−26702 K/T) s–1

[38]

CH2O + H + CH3 +SiO2

k(T) = 3.0×1016 exp(−49796 K/T) s−1

[38]

k(T) = 3.3×10−11 exp(−2514 K/T) cm3s−1

[38]

k(T) = 1.5×10−11 exp(−5028 K/T) cm3s−1

[38]

H + HSi(OCH3)3 OSi(OCH3)3 Si(OCH3)3

H2 + Si(OCH3)3

OSi(OCH3)2 + CH2O + H CH3 + OSi(OCH3)2

CH2OSiO(OCH3) OSi(OCH3)2

H + OSi(OCH3)2

H2 + CH2OSiO(OCH3)

CH3 + OSi(OCH3)2

CH4 + CH2OSiO(OCH3)

CH3OH(+M)

CH3+OH(+M)

k∞(T) = 2.1×1018 T–0.61 exp(−46571 K/T) s−1 k0(T) = 2.5×1019 T–6.99 exp(−49314 K/T) cm3s−1 α = 0.4748/T*** = 35580/T* = 1116/T** = 9023

[39][40]

CH3OH(+M)

CH2(S) + H2O(+M)

k∞(T) = 3.1×1018 T–1.0 exp(−46154 K/T) s–1 k0(T) = 2.4×1023 T–8.2 exp(−50031 K/T) cm3s–1 α = 2.545/T*** = 3290/T* = 47320/T** = 47110

[39][40]

CH3OH(+M)

CH2OH+H(+M)

[39][40] k∞(T) = 7.9×10–3 T5.0 exp(−42508 K/T) s–1 42 –7.2 3 –1 k0(T) = 5.6×10 T exp(−52957 K/T) cm s α = −73.91/T*** = 37050/T* = 41500/T** = 5220

H2 + M C2H6(+M)

H+H+M CH3 + CH3 (+M)

k(T) = 7.6×10–5 T–1.4 exp(−52539 K/T) cm3s–1

[41]

k∞ = 8.03×1028 T–3.52 exp(−47983 K/T) s–1 k0 = 4.65×1048 T–15.10 exp(−54222 K/T) cm3s–1 α = 0.21/T*** = 1.00×10–30/T* = 1.00×1030

[42]

It was attempted to conduct the H-ARAS experiments at nearly pseudo-first-order conditions. Therefore, initial mole fractions of Si(OCH3)4 were much higher than those of C2H5I, i.e., x(Si(OCH3)4)0 ∼ 19 x(C2H5I)0. Hence, a pseudo-first-order analysis was carried out to determine total rate constants for (R1) as an initial estimate in the reaction mechanism. Best-fit simulated profiles to the experimental data were then obtained by variations to these pseudo-first-order rate constants. [H]t profiles from two H + Si(OCH3)4 experiments are shown in Fig. 3 together with pseudo-first-order analyses.

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Fig. 3. Left: Measured [H]t profiles; experiments were conducted with x(C2H5I)0 = 0.43 ppm and x(Si(OCH3)4)0 = 7.90 ppm at T = 1111 K and p = 1.24 bar (top) as well as T = 1226 K and p = 1.36 bar (bottom). Right: Pseudo-first-order plots of these particular experiments; with [Si(OCH3)4]0 = 6.387×1013 cm–3 (top) and 6.348×1013 cm–3 (bottom) and corresponding slopes of d[log[H]]/dt = 1260 s–1 and 1740 s−1, rate constants of k1 = 4.54×10−11 cm3s–1 and 6.31×10–11 cm3s–1 were derived.

The [H]t profiles were then simulated using the Table 1 mechanism, which is illustrated in the left panel of Fig. 4 (solid line). Changes in the best-fit rate constant k1 by ±25% (dotted lines) degrade the agreement of the simulated and the experimental [H]t profile. The right panel in Fig. 4 shows the H-atom sensitivity analysis for the corresponding experiment.

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Fig. 4. Left: Brute-force sensitivity analysis for (R1) for the experiment at T = 1226 K presented in Fig. 3. The concentration profiles were calculated with the reaction mechanism provided in Table 1. Solid line: best fit for k1; dotted curves: k1×1.25 and k1×0.75. Right: Local H-atom sensitivity analysis for this particular experiment. The local H sensitivity S is defined as S = (dxH/dki).

It can be seen that (R1) shows the largest sensitivity over the observation period of 1000 µs. Reactions of minor sensitivity are the two C2H5I decomposition channels, (R3a) and (R3b). At t > 500 µs, the unimolecular channel

Si(OCH3)4 = CH3 + OSi(OCH3)3

(R4a)

contributes to H-atom formation, since the intermediate radical OSi(OCH3)3 yields CH3O and OSi(OCH3)2, whereupon CH3O radicals rapidly dissociate to give CH2O + H. However, the primary Si(OCH3)4 decomposition channel is a four-center elimination (R4b):

Si(OCH3)4 = CH3OH + CH2OSi(OCH3)2

(R4b)

According to Chu et al.38, the 4-center-elimination yields a dipolar intermediate, which rapidly isomerizes to form the molecules CH3OH and CH2OSi(OCH3)2. At T < 1240 K, the branching ratio BR4a, BR4a = k4a/(k4a+k4b), is less than 10%37-38. Up to t < 500 µs, the decay of experimental [H]t profiles can be simulated only by adjusting the value of k1. In order to avoid ambiguities regarding best-fit simulation of k1, all the experiments have been carried out at T < 1240 K so that the influence of the bond-fission channel R4a is suppressed. The limited temperature range 13



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is also set by the decomposition characteristics of the H-atom-precursor C2H5I that dissociates on a suitable time scale at temperatures near 1100 K only. Table 2 provides a listing of the experimental conditions as well as experimental rate constants obtained from simulations. The supporting information (Table S1 and Fig. S1) also includes a comparison between simulated best-fit rate constants and rate constants obtained from the pseudo-first-order analysis.

Table 2. Summary of experimental conditions for H + Si(OCH3)4 experiments. Si(OCH3)4 / ppm 7.9 8.6 8.6 8.6 8.6 7.9 8.8 7.9 8.8 8.8

C2H5I / ppm 0.43 0.42 0.42 0.42 0.42 0.43 0.45 0.43 0.45 0.45

p / bar 1.24 1.37 1.28 1.34 1.45 1.34 1.40 1.36 1.45 1.40

T/K 1111 1160 1161 1164 1181 1201 1222 1226 1227 1238

k1 / cm3s−1 4.57×10−11 4.82×10−11 4.82×10−11 4.65×10−11 5.48×10−11 5.56×10−11 5.40×10−11 6.31×10−11 5.40×10−11 5.81×10−11

The aim of the present work is to compare the reactivity of Si(OCH3)4 with the reactivity of CH3OCH3 with respect to H abstractions. In both molecules, only primary C-H bonds are present. Since Si(OCH3)4 und CH3OCH3 have different number of C-H bonds, we try to compare reactivity per C-H bond, i.e., in the present work, H-abstraction rate constants per C-H bond will be compared. The H-ARAS experiments described above result in total rate constant values for k1, k1,total. Since Si(OCH3)4 exhibits twelve C-H bonds, the average rate constant per C-H bond, k1,C-H, is ktotal divided by the number of C-H bonds: k1,C-H = k1,total/12. In case of symmetric molecules like C(CH3)4 or Si(CH3)4 that belong to the Td point-group, all twelve C-H bonds are equivalent, i.e., for H abstractions kC-H = ktotal/12. In contrast to these compounds, the geometry optimization for Si(OCH3)4 results in an energy-minimum structure that belongs to the C1 pointgroup. Therefore, treating all twelve C-H bonds in Si(OCH3)4 as being equal might not be an appropriate treatment for TST predictions. This is illustrated in Fig. 5.

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Fig. 5. Depending on the position from which C-H bond H abstraction takes place, one obtains three different TST predictions (per C-H bond) that are denominated as k1,C-H’, k1,C-H’’, and k1,C-H’’’. In the presented structure of Si(OCH3)4, the C-H bonds to which these TST calculations refer are marked with arrows. The circle symbols in the Arrhenius plots refer to rate constants k1 measured in this work.

Figure 5 shows the deviations between TST predictions in dependence of the abstracted H atom from the corresponding C-H bond. In Figure 5, as well as in the other Arrhenius diagrams presented in this article, rate constant data are shown from 660 to 2000 K for the purpose of better visualizing differences in experimental and theoretical k(T) values. Arrhenius plots showing k(T) predictions from 300 up to 2000 K are included in the supporting information (Figs. S3 and S4). The CH3 group examined in Fig. 5 has three C-H bonds, which we denote as C-H’, C-H’’, and CH’’’. H abstraction from the C-H’ bond yields a theory-based prediction k1,C-H’, H abstraction from the C-H’’ results in the k1,C-H’’ prediction, and k1,C-H’’’ is the result of H abstraction from C-H’’’. Abstraction from each of the marked C-H bond shows slightly different barrier heights, i.e., energetic barriers for H abstractions from C-H’, C-H’’, and C-H’’’, obtained from classical energies of the stationary points from the H + Si(OCH3)4 potential energy surface (PES), are 34.09, 31.11, and 34.03 kJ/mol. Molecular properties of the stationary points of the H + Si(OCH3)4 PES for these three C-H bonds are presented in Tables S2a–c in the supporting information. The corresponding Si(OCH2)(OCH3)3 radicals, formed by the H abstractions from these three C-H bonds, do not show substantial energy differences, i.e., no matter from which

15



C-H bond an H atom is abstracted, the energy difference between the corresponding Si(OCH2)(OCH3)3 radicals is less than 0.8 kJ/mol. Therefore, the primary reasons for different TST predictions k1,C-H’ - k1,C-H’’’ are attributed to (a) differences in the energy-barrier heights, in particular between H abstractions from C-H’ and C-H’’’ bonds on the one side and the C-H’’ bond on the other side, and (b) to numerical differences between the vibrational partition functions of the transition-state structures. Assuming equivalence of the four CH3 groups, there are three types of C-H bonds with different reactivity towards H abstraction: C-H’, C-H’’, and C-H’’’. From each type, there are four bonds, i.e., for reaction R1, k1,total = 4 × k1,C-H’ + 4 × k1,C-H’’ + 4 × k1,C-H’’’. Per C-H bond, the average rate constant k1,C-H weighted by the contribution of each type of C-H bond to k1,total is given by k1,C-H = (1/3) × k1,C-H’ + (1/3) × k1,C-H’’ + (1/3) × k1,C-H’’’. Figure 6 shows a comparison between k1,C-H from TST calculations and the experimental rate constant data, k1,C-H = k1,total/12.

Fig. 6. Arrhenius plot of the H + Si(OCH3)4 experimental rate constants for H abstraction per C-H bond. Circle symbols represent experimental rate constant data k1,C-H, whereas the red solid curve refers to TST calculations; k1,C-H from theory is calculated by considering the weighted contributions of the different CH bonds to k1,C-H (see text). Dashed lines represent TST predictions assuming an uncertainty of ± 4.2 kJ mol−1 in the barrier heights of H-abstraction reactions. Error bars represent uncertainties of ±25%.

The G4-TST calculation is in excellent agreement with the present experimental results, i.e., the theoretical rate constants k1,C-H are on average 20% larger than the experimental values of k1,C-H.

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The overall uncertainty of measured rate constants was estimated to be ±25%. The dashed lines in Fig. 6 represent TST calculations, in which the energetic barrier heights of TST calculations were varied by ±4.2 kJ mol−1. This uncertainty range of barrier height was chosen since the G4 composite method is supposed to reproduce reference thermochemical data from Active Thermochemical Tables to within “near-chemical-accuracy”, i.e., 4.2 kJ mol−1. Over the temperature range 1111–1238 K, the experimental total H-abstraction rate constants k1,total can be represented by the Arrhenius equation (1a)

k1,total(T) = 10−9.16±0.24 exp(–25.5±5.6 kJ mol−1/RT) cm3s−1

(1a)

Accordingly, experimental average H-abstraction rate constants per C-H bond, k1,C-H, are then – as explained above – obtained by dividing k1,total by the number of available C-H bonds in Si(OCH3)4:

k1,C-H(T) = 10−10.24 exp(–25.5 kJ mol−1/RT) cm3s−1

(1b)

Over the experimental temperature range, the G4-based total H-abstraction rate constants are described by the Arrhenius equation (2a):

k1,total(T) = 2.35×10-9 exp(–39.2 kJ mol−1/RT) cm3s−1

(2a)

Over the extended temperature range of 500–2000 K, TST calculated rate H-abstraction constants per C-H bond are described to within ±4% by the Arrhenius equation (2b):

k1,C-H(T) = 3.30×10−19 T2.502 exp(–14.89 kJ mol−1/RT) cm3s−1

(2b)

A direct comparison between k1,total data from measurements and theory over the 1100–1240 K temperature range is included in the supporting information (Fig. S2). The comparison between experimental data and theory suggests that at least at high temperatures, T > 1000 K, the G4 method results in reliable rate constant predictions. However, the intention of this work is to 17



compare H abstraction reactivity between Si(OCH3)4 and CH3OCH3 in order to get an indication if CH3OCH3 is a reasonable reactivity analogy to Si(OCH3)4. Therefore, it is necessary to compare abstraction rate constants per C-H bonds and to check if the G4 method is also able to reasonably predict rate constant values for R2. Like Si(OCH3)4, the molecule CH3OCH3 has only primary C-H bonds, but it belongs to the C2v point-group and has an intramolecular mirror plane of symmetry. Two C-H bonds are within this mirror plane, whereas the other four C-H bonds are symmetrically out of this mirror plane. The in-plane C-H bonds are denoted with the acronym ip, whereas the out-of-plane C-H bonds are denoted with the abbreviation oop. Zhou et al.43 demonstrated that ip and oop C-H bonds have different reactivity towards H abstraction by OH radicals due to the formation of different hydrogen-bonded complexes between an OH radical and CH3OCH3. In case of propane (C3H8), which has the analog structure to CH3OCH3 and which also belongs to the C2v point group, Sivaramakrishnan et al.44 demonstrated that for H-atomabstractions by H radicals, ip and oop C-H bonds result in different TST predictions. Therefore, we checked if this also applies for CH3OCH3.

Fig. 7. Comparison between G4-based TST predictions for H abstractions from ip and oop C-H bonds by H atoms and measured rate constants for (R2). Square symbols in the Arrhenius plot (right) represent experimental k2,C-H data obtained by Takahashi et al.45 in H-ARAS shock-tube experiments. Abstraction from an oop or ip C-H bond leads to corresponding theoretical k2,C-H(oop) and k2,C-H(ip) values. The blue solid and the orange dotted line refer to present theoretical values of k2,C-H(ip) and k2,C-H(oop), respectively.

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According to Fig. 7, the results of the present TST calculations suggest that for abstractions by H atoms, ip and oop C-H bonds do not show substantially different reactivity, i.e., the difference between k2,C-H(oop) and k2,C-H(ip) is less than 5%. Therefore, regarding (R2), the ip and oop C-H bonds in CH3OCH3 are considered as equivalent. So far, one data set of directly determined high-temperature rate constants for (R2) has been reported. Takahashi et al.45 measured depletion of H atoms behind reflected shock waves also applying the highly sensitive H-ARAS technique. Their experimental data are shown in the Arrhenius plot in Fig. 8 by the square symbols. In order to obtain abstraction rate constants per C-H bonds, k2,C-H, the total rate constants k2,total reported by Takahashi et al.45 were divided by the number of C-H bonds: k2,C-H = k2,total/6. This is justified, since both bond types, ip and oop C-H bonds can be regarded as equivalent with respect to H abstractions by H atoms. Again, the present G4-based TST prediction is in excellent agreement with these experimental data, i.e., theoretical values are approximately 10% lower than the experimental data from Takahashi et al.45. Sivaramakrishnan et al.46 performed H-ARAS shock-tube experiments on the thermal decomposition of CH3OCH3. For CH3OCH3/Kr mixtures with initial CH3OCH3 mole fractions of up to 10 ppm, their experiments also revealed significant sensitivity on (R2). Based on a limited review of their own high-temperature data and those from Takahashi et al.45 as well as available low temperature data, Sivaramakrishnan et al.46 derived an Arrhenius expression for k2,total covering the temperature range from 273–1465 K. This recommended rate constant is included in the Arrhenius diagram in Fig. 7 as red dashed line. From room temperature up to 500 K, the present TST prediction deviates from the recommended data for k2,total (see Fig. S3 in the supporting information), which is probably related to the problem, that B3LYP functionals are known to underestimate imaginary frequencies. From room temperature up to 500 K, the present TST prediction deviates from the recommended data for k2,total, which is probably related to the problem that B3LYP functionals are known to underestimate imaginary frequencies. However, at temperatures above 500 K, the present TST prediction reproduces the available experimental and the recommended rate-constant data remarkably well. Figure 8 shows a comparison between the H-abstraction rate constants k1,C-H and k2,C-H.

19



Page 20 of 25

Fig. 8. Experimental data and TST predictions for rate constants of (R1) and (R2). Circles are experimental data for k1,C-H obtained in this work; triangles are calculated k2,C-H values using the experimentally-based two-parameter Arrhenius expression for (R2) from Takahashi et al.45. The red solid curve represents TST calculations for k1,C-H; the green-dashed curve refers to the rate-constant evaluation from Sivaramakrishnan et al.46 on (R2).

Fig. 8 shows that the experimental high-temperature rate constants k1,C-H and k2,C-H are quite similar, i.e., k1,C-H ~ 1.5×k2,C-H. The same applies for the TST calculations: k(TST)1,C-H ~ 1.5×k(TST)2,C-H. The TST prediction for k1,C-H is within the uncertainty of the high-temperature experimental data sets of both (R1) and (R2). This finding suggests that in terms of H abstractions, CH3OCH3 is a reasonable reactivity analogy for Si(OCH3)4. Si(OCH3)4 is only one possible alkoxy-silane that can be used as a precursor for the production of silicon-containing nanoparticles in combustion synthesis. Other, more prominent compounds are, for example, tetraethoxy-silane (Si(OC2H5)4), hexamethyl-disiloxane

((CH3)3SiOSi(CH3)3),

cyclohexamethyl-trisiloxane

(D3)

and

cyclooctamethyl-tetrasiloxane (D4). Making reactivity analogies between siloxanes and corresponding oxygenated hydrocarbons would be another possibility to obtain reasonable estimates for H-abstraction rate constants. As CH3OCH3 seems to be a suitable reactivity analogy to Si(OCH3)4, diethyl ether (C2H5OC2H5) could be a useful analogy to Si(OC2H5)4. In the same way, di-tertbutyl-ether or tertbutyl-methyl-ether could be reasonable reactivity analogies in order to obtain educated guesses about rate constants for the H abstractions H/OH/CH3 + (CH3)3SiOSi(CH3)3. However, we think that for further explorations regarding the possibility of

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reactivity analogies and the development of structure–activity relationships of silanes and siloxanes, high level ab initio TST studies in combination with further experimental elementary kinetic investigations are required.

4. Conclusions The shock-tube technique was used to determine rate constants for the H abstraction H + Si(OCH3)4. Experiments were performed over the temperature range 1111–1238 K at pressures of ∼1.3–1.4 bar behind reflected shock waves. C2H5I was used as a thermal source for H atoms. The highly sensitive H-ARAS diagnostic was used to probe the kinetics of this reaction. The measurements have been supported by G4-based TST calculations. The results show that in contrast to Si(CH3)4, which belongs to the Td point group, not all of the C-H bonds in Si(OCH3)4 are equivalent. TST calculations indicate that the four CH3 groups in Si(OCH3)4 can be regarded as equivalent, whereas each C-H bond in each CH3 group has different reactivity towards H abstraction by H atoms. Therefore, three types of C-H bonds equally contribute to the total abstraction rate constant. By considering the different contribution of different C-H bonds, rate constants derived from theory were in excellent agreement with the present experimental data. To the best of our knowledge, this work provides the first experimental rate constant data on the title reaction. In the course of this investigation, the possibility of applying CH3OCH3 as a H-abstraction reactivity analogy to H + Si(OCH3)4 is explored. At temperatures above 500 K, TST calculations based on energy barrier heights and molecular properties from G4 ab initio calculations were in very good agreement with available high temperature rate constant data for the reaction H + CH3OCH3. A comparison between theoretical and experimental rate constants of the reactions H + Si(OCH3)4 and H + CH3OCH3 suggests that CH3OCH3 can be considered as a reasonable Habstraction reactivity analog to Si(OCH3)4. Expanding the idea of reactivity analogies between silanes/siloxanes and corresponding hydrocarbons/oxygenated hydrocarbons would be useful for obtaining useful rate constant estimations for H abstractions, which are one of the most important class of reactions under the conditions in combustion synthesis processes of silica. 21



Acknowledgement Financial support by the German Research Foundation within the framework of the DFG research unit FOR 2284 (SCHU1369/25) is gratefully acknowledged. We also wish to thank Dr. Jürgen Herzler (Duisburg) and Professor Alexander Eremin (Moscow) for helpful discussions of this work.

Supporting Information Available: Listing of experimental rate constants from pseudo-firstorder-analysis, Arrhenius diagrams showing TST-predictions over an extended temperature range (300 - 2000 K) and listings of molecular properties (frequencies, moments of inertia, and energies) from stationary points on the H + Si(OCH3)4 potential energy surface.

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High-Temperature Rate Constants for the Reaction of Hydrogen

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