Gas-phase oxidation of vinyltrifluorosilane with nitrogen dioxide under the action of a pulse CO2 laser

Article abstract of DOI:10.1134/S0023158410050022

A chemical reaction between C₂H₃SiF₃ and NO₂ induced by radiation from a pulse CO₂ laser was studied by mass spectrometry and IR spectroscopy. The composition of gaseous products was determined. A macrokinetic approach was developed to study bimolecular reactions initiated by pulsed IR radiation. The procedure developed allowed us to answer the question of whether the test reaction occurs under conditions when the molecules of only one reactant are vibrationally excited or under conditions of equal vibrational temperatures. The use of this approach to the reaction between C₂H₃SiF₃ and NO ₂ demonstrated that its acceleration was due to the equilibrium heating of the system.

Full text of DOI:10.1134/S0023158410050022

ISSN 0023ꢀ1584, Kinetics and Catalysis, 2010, Vol. 51, No. 5, pp. 624–634. © Pleiades Publishing, Ltd., 2010.
Original Russian Text © P.S. Dement’ev, P.V. Koshlyakov, E.N. Chesnokov, 2010, published in Kinetika i Kataliz, 2010, Vol. 51, No. 5, pp. 650–660.
GasꢀPhase Oxidation of Vinyltrifluorosilane with Nitrogen Dioxide
under the Action of a Pulse CO2 Laser
P. S. Dement’ev, P. V. Koshlyakov, and E. N. Chesnokov
Institute of Chemical Kinetics and Combustion, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
eꢀmail: dementyev@kinetics.nsc.ru
Received December 21, 2009
Abstract—A chemical reaction between C2H3SiF3 and NO2 induced by radiation from a pulse CO2 laser was
studied by mass spectrometry and IR spectroscopy. The composition of gaseous products was determined. A
macrokinetic approach was developed to study bimolecular reactions initiated by pulsed IR radiation. The
procedure developed allowed us to answer the question of whether the test reaction occurs under conditions
when the molecules of only one reactant are vibrationally excited or under conditions of equal vibrational
temperatures. The use of this approach to the reaction between C2H3SiF3 and NO2 demonstrated that its
acceleration was due to the equilibrium heating of the system.
DOI: 10.1134/S0023158410050022
INTRODUCTION
thermal or nonthermal, that is, whether it is due to a
nonequilibrium concentration of vibrationally excited
molecules or equilibrium heating. As of now, it has
been found that, with the use of continuousꢀwave IR
lasers, there is a limiting pressure above which radiaꢀ
tion can affect the occurrence of gasꢀphase reactions
only because of an increase in the equilibrium temperꢀ
ature. The characteristic value of this limiting pressure
varies from several tens to hundreds of Pa [6, 7]. The
use of pulse lasers eliminates this restriction and makes
it possible to exert a nonthermal effect of laser radiaꢀ
tion at higher pressures. However, the problem of a
thermal or nonthermal character of the effect of radiꢀ
ation should be individually solved for each particular
reaction.
The use of highꢀpower IR radiation makes it possiꢀ
ble to generate superequilibrium concentrations of
vibrationally excited molecules, thereby stimulating
the occurrence of chemical reactions [1]. The appearꢀ
ance of new frequencyꢀtuned IR laser radiation
sources, such as powerful semiconductor lasers and
free electron lasers [2], is causing a rebirth of interest
in these studies. The selective stimulation of chemical
reactions used for isotope separation or laser purificaꢀ
tion is the most attractive capability.
There are two essentially different schemes for conꢀ
trolling chemical processes with the use of IR laser
radiation. In the first case, laser radiation causes suffiꢀ
ciently strong molecular excitation to result in dissociꢀ
ation [3]. A unimolecular reaction is stimulated in this
manner. This suggests the absorption of a large numꢀ
ber of laser photons (the phenomenon of multiphoton
IR excitation) or the excitation of high vibrational levꢀ
els upon the absorption of a laser photon (overtone
excitation).
The other approach consists in the use of comparꢀ
atively low molecular excitation, which does not
cause dissociation but increases the rate of the subseꢀ
quent reactions with the participation of the excited
molecule. This approach can be referred to as the
laser control of bimolecular reactions. The most
interesting results in this area were obtained in a
study of the interaction of small molecules with
atoms and free radicals [4].
The laser acceleration of a bimolecular reaction
between stable polyatomic molecules is of the greatest
practical importance. Studies in this area have been
started a long time ago [5]. At the outset, the question
In this work, we propose a procedure for kinetic
analysis of a bimolecular reaction initiated by pulse
laser radiation. It allowed us to study reactions occurꢀ
ring either under vibrational nonequilibrium condiꢀ
tions or under full equilibrium conditions. This proceꢀ
dure was used to study of a model reaction of vinyltriꢀ
fluorosilane (C2H3SiF3) with nitrogen dioxide (NO2).
As a model, this reaction has a number of advantages.
The C2H3SiF3 is very efficiently excited by CO2 laser
radiation because of the presence of the SiF3 group [8].
At the same laser radiation density, C2H3SiF3 absorbs
more energy than SF6 by a factor of 3–5 [9]. At the
same time, the presence of the unsaturated –C2H3
fragment in the molecule imparts a certain chemical
activity to this molecule. It is believed that C2H3SiF3
enters into reactions at the double bond similarly to
hydrocarbons from the ethylene series. In particular,
vinylfluorosilane can be oxidized by nitrogen dioxide.
The presence of an unpaired electron in the NO2 molꢀ
arose as to whether the action of IR laser radiation is ecule impart a high reactivity to it [10
⎯13].
624

GASꢀPHASE OXIDATION OF VINYLTRIFLUOROSILANE WITH NITROGEN DIOXIDE
625
It was found experimentally that C2H3SiF3 did not
react with NO2 at room temperature and a reactant
pressure of ~102 Pa. However, the irradiation of a mixꢀ
ture of C2H3SiF3 and NO2 with a pulse CO2 laser
caused irreversible chemical changes. The energy denꢀ
sity used in this case was insufficient for the dissociaꢀ
tion of vinyltrifluorosilane; this fact suggests a chemiꢀ
cal character of its interaction with nitrogen dioxide.
[C2H3SiF3], arb. units
1.0
0.9
1
2
3
EXPERIMENTAL
0.8
0.7
The experiments were performed under batch conꢀ
ditions at room temperature; the pressure of gas samꢀ
ples was no higher than 103 Pa. A glass vacuum system,
which was designed for the synthesis, storage, and
puffing of substances, was equipped with a cylindrical
Pyrex cell 42 cm in length and 3 cm in diameter with
planeꢀparallel windows of NaCl. The cell was conꢀ
nected to the ion source of an MX 1303 magnetic mass
0
100
200
Pulse number
300
Fig. 1. Consumption of C H SiF upon the irradiation of
2
3
3
the reaction cell with a CO laser: (
1
) a mixture of
C H SiF (60 Pa) and NO (240 Pa); ( ) individual
) a mixture of C H SiF (47 Pa) and
2
2
3
2
2
3
3
3
3
2
spectrometer through a smallꢀdiameter (~20 m) diaꢀ
µ
C H SiF (60 Pa); (
3
2
3
phragm; this allowed us to monitor the composition
the sample at any point in time. It was also possible to
automatically record the spectra obtained in the
course of periodical scanning over a specified range of
mass numbers. The pressure in the system was conꢀ
trolled with a Baratron R227A pressure gage, and the
temperature was measured with a thermocouple senꢀ
sor. The synchronized recording of a p–T diagram
allowed us to obtain information on the phase compoꢀ
nent composition of the sample.
SO (200 Pa). A laser with a pulse energy density of
0.56 J/cm was tuned to the R12 line (970.5 cm ); the
pulse repetition frequency was 0.5 Hz.
2
2
–1
employing the hybrid density functional theory
DFT/b3lyp method with the 6ꢀ311++ basis set. The
parameters of the transition complex were determined
using the QST2 procedure.
The cell was arranged along the optical axis of a
pulse CO2 laser with energy varied to 3 J/pulse [14].
The laser pulse had a shape characteristic of these
lasers: the main peak with a duration of 200 ns was
accompanied by a tail with a duration of about 800 ns.
A central portion was separated from the laser beam
using a diaphragm 1 cm in diameter and used for the
irradiation of the reaction cell. Laser radiation was not
focused. The radiation energy was measured using a
power meter and a pyroelectric detector both before
and behind the reaction cell.
RESULTS
Acceleration of the Reaction of C2H3SiF3
with NO2 under the Action of Laser Radiation
We found that C2H3SiF3 and NO2 do not react with
each other at room temperature. For this purpose, we
recorded the mass spectrum and p–T diagram of a
mixture of C2H3SiF3 and NO2 at partial pressures of
70 Pa and allowed the mixture to stand in the reaction
cell for 1 h; then, we performed a repeated analysis,
which demonstrated the absence of changes from the
system.
The preparation of vinyltrifluorosilane was
described elsewhere [8]. Nitrogen dioxide used in this
study was prepared by the reaction 2NO + O2
2NO2 and purified by repeated freeze–thawing fracꢀ
tionation. A mixture of the substances was introduced
into the cell and irradiated with a laser. To control the
degree of conversion and to determine the composiꢀ
tion of products, IR spectroscopic analysis was perꢀ
formed on a Bruker Vector 22 Fourier transform specꢀ
trometer with a resolution of 1 cm–1. The substances
were analyzed in a cell 18 cm in length and 3 cm in
The action of CO2 laser radiation caused a chemiꢀ
cal reaction in the C2H3SiF3–NO2 system. Figure 1
shows changes in the concentration of vinyltrifluorosiꢀ
lane upon the irradiation of its mixture with nitrogen
dioxide in the absence of multiphoton dissociation.
The concentration of vinyltrifluorosilane was deterꢀ
mined by mass spectrometry from a signal with m/z =
+
112 due to the molecular ion
. It can be seen
C2H3SiF3
that the degradation of C2H3SiF3 did not occur at an
diameter. The IR spectra were measured over a range energy density of 0.56 J/cm2 in a laser tuned to the R12
of 400–4000 cm–1 before and after laser irradiation.
line (970.54 cm–1) near a linear absorption maximum
of C2H3SiF3 (antisymmetric vibration ν8 (a') and antiꢀ
symmetric vibration ν16 (a'')) [8]. However, in the
presence of NO2, the concentration of C2H3SiF3
Quantumꢀchemical calculations for the geometry
optimization of reactants, products, and intermediate
species and a search for the transition state were perꢀ
formed using the Gaussianꢀ98 program package [15] began to decrease as the laser was turned on.
KINETICS AND CATALYSIS Vol. 51
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626
DEMENT’EV et al.
Absorption, arb. units
0.30
1
2
3
C2H3SiF3
0.25
0.20
0.15
0.10
0.05
0
NO2
860 870 880 890 900 910
1580 1600 1620 1640 1660
1
Wavenumber, cm−
Fig. 2. Fragments of the IR spectrum of a mixture of vinyltrifluorosilane (40 Pa) and nitrogen dioxide (230 Pa): (1) before irradiꢀ
2
ation, (2) after irradiation for 20 min, and (3) after irradiation for 40 min. A laser with an energy of 0.56 J/cm was tuned to the
R12 line; the pulse repetition frequency was 0.5 Hz; the cell length was 18 cm.
At a total pressure of 300 Pa in a mixture, C2H3SiF3
Product Composition
molecules undergo several collisions during the time
of a laser pulse. To exclude the explanation of the
observed results by a decrease in the efficiency of the
multiphoton excitation of C2H3SiF3, which leads to
dissociation, we performed experiments in which a
knowingly inert component—sulfur dioxide—was
the second component of a mixture. As can be seen in
Fig. 1, C2H3SiF3 was not consumed upon the addition
of sulfur dioxide. The numbers of the degrees of freeꢀ
dom in SO2 and NO2 molecules are the same; the
vibrational frequencies of these molecules are also
comparable. Assuming that collisions with SO2 and
NO2 molecules equally affect the process of multiphoꢀ
ton excitation, we conclude that the dissociation of
C2H3SiF3 does not occur both in a mixture and in an
individual state.
The massꢀspectrometric analysis of a reaction mixꢀ
ture during and after laser irradiation suggests its comꢀ
plex composition. Many new peaks appear in the mass
spectrum. Attempts to perform the lowꢀtemperature
fractionation of a reaction mixture were unsuccessful:
after freezing to –196°C and repeated puffing to the
cell, new lines disappeared from the mass spectrum of
the mixture. It is likely that siliconꢀcontaining prodꢀ
ucts form nonvolatile polymers in a condensed phase.
The main result of the lowꢀtemperature fractionation
was the identification of nitrogen monoxide, whose
vapor has a sufficiently high volatility at a liquid nitroꢀ
gen temperature.
The newly formed peaks in the mass spectrum were
attributed by comparing with the available mass specꢀ
tra of substances taking into account the atomic weight
composition of the starting mixture (Table 1). Ethinylꢀ
trifluorosilane (C2HSiF3) and silicon tetrafluoride
The occurrence of a chemical reaction was also
supported by IRꢀspectrometric analysis. Figure 2
shows changes in the IR spectrum of a mixture of
C2H3SiF3 and NO2 in the course of laser irradiation. A
band at 890 cm–1 corresponds to symmetrical vibraꢀ
tions in the SiF3 group of the vinyltrifluorosilane molꢀ
ecule [8], whereas absorption at 1615 cm–1 belongs to
the antisymmetric stretching vibration of nitrogen
dioxide. Upon the laser irradiation of a mixture of
C2H3SiF3 with NO2, the concentrations of both of the
components decreased.
(
SiF4) belong to the siliconꢀcontaining products (their
mass spectra are known). Compounds containing the
Si–O bond were also detected, namely, trifluorosilꢀ
anol (HOSiF3) and hexafluorodisiloxane (O(SiF3)2).
In addition, a product formally corresponding to the
addition of an oxygen atom to vinyltrifluorosilane was
identified; hypothetically, this is vinyl trifluorosilyl
ether (F3Si–O–CH=CH2). Reacted nitrogen dioxide
was mainly converted into the monoxide NO.
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GASꢀPHASE OXIDATION OF VINYLTRIFLUOROSILANE WITH NITROGEN DIOXIDE
627
Table 1. Identification of products of the reaction of CH3SiF3 with NO2 based on the results of massꢀspectrometric analysis
Mass number (m/z)
Ion
F3Si–O–SiF3+
F3Si–O–SiF2+
Product
186
167
128
Hexafluorodisiloxane (F3Si–O–SiF3)
Hexafluorodisiloxane (F3Si–O–SiF3)
F3Si–O–CH=CH2+
F3Si–O–C2H+
Vinyl trifluorosilyl ether
Vinyl trifluorosilyl ether
126
110
F3Si–C
≡
CH+
Ethyltrifluorosilane (F3Si–C
Silicon tetrafluoride (SiF4)
Trifluorosilanol (F3Si–OH)
–
≡CH)
SiF4+
104
102
85*
83
F3Si–OH+
SiF3+
F2Si–OH+
N2O+, CO2+
Trifluorosilanol (F3Si–OH)
44
Nitrogen hemioxide or carbon dioxide
43
30
29
C2H3O+
NO+
Vinyl trifluorosilyl ether
Nitrogen monoxide (NO)
Vinyl trifluorosilyl ether
HCO+
CO+, N2+
28
26
Nitrogen hemioxide, carbon dioxide, or nitrogen
C2H+
Acetylene (C2H2)
2
25
18
C2H+
H2O+
Acetylene (C2H2)
Water (H2O)
* Uncharacteristic peak, which can be due to various molecules.
The quantitative analysis of a mixture is difficult to tion of vinyltrifluorosilane was 34%, which correꢀ
perform because of the impossibility of lowꢀtemperaꢀ sponds to a partial pressure of 22 Pa under constant
ture separation, the absence of the published mass volume conditions. The partial pressures of the resultꢀ
ing ethinyltrifluorosilane and SiF4 were 2.8 and 11 Pa,
respectively.
spectra of individual substances, and the mutual
superposition of peaks due to various components. We
attempted to perform gasꢀchromatographic analysis in
order to separate and identify the products. However,
because of the low concentrations of mixture compoꢀ
nents after dilution with a carrier gas, we failed to
obtain any additional information.
Reaction Mechanism
The composition and nature of the final products
SiF4, C2H2, and C2HSiF3) suggest a complex reaction
(
The main siliconꢀcontaining products were identiꢀ
fied by IR spectroscopy in the region of characteristic
absorption due to Si–F vibrations. Figure 3 shows the
IR spectra of reaction products obtained by subtractꢀ
ing the spectrum of unreacted C2H3SiF3 from the
spectra of the reaction mixture before and after irradiꢀ
ation. The individual spectra of ethinyltrifluorosilane
mechanism. Published data on the formation of diniꢀ
tro derivatives are available [10]. It is likely that an
analogy between vinyltrifluorosilane and unsaturated
hydrocarbons is incomplete. The course of the reacꢀ
tion in our experiments is closest to data published by
Chao and Jaffe [11], who proposed a reaction scheme
for ethylene oxidation with nitrogen dioxide
(Scheme 1). At the first step, the electrophilic addition
of the NO2 molecule occurs with double bond opening
(
C2HSiF3) and silicon tetrafluoride (SiF4) are also
shown. It can be seen that bands at 893.0 and
998.1 cm–1 in the spectrum of products belong to ethiꢀ and the formation of a carboradical. It is believed that,
nyltrifluorosilane, whereas SiF4 makes the main conꢀ in a gas phase, intermediate
had time to rearrange
tribution to absorption at 1029.5 cm–1. The consumpꢀ before a collision with the next NO2 molecule. In this
1
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628
DEMENT’EV et al.
Absorbance, arb. units
Before irradiation
After irradiation
1029.5
0.15
0.10
998.1
0.05
Products
894.0
SiF4
C2H3SiF3
0
860 880 900 920 940 960 980 1000 1020 1040 1060
1
Wavenumber, cm−
Fig. 3. Identification of reaction products based on IR spectra. Top: the spectra of the reaction mixture of C H SiF (65 Pa) and
2
3
3
2
NO (285 Pa) before and after laser irradiation with an energy density of 0.51 J/cm . Bottom: the spectrum of products minus the
2
contribution of unreacted C H SiF and the spectra of C HSiF and SiF .
2
3
3
2
3
4
case, a nitrogen monoxide molecule is eliminated and Rearrangement with the elimination of an NO moleꢀ
biradical 2 is formed. A further rearrangement of 2 can
result in the formation of stable products—epoxide
and acetaldehyde.
cule should be similar to that in the case of ethylene;
however, the subsequent rearrangement of biradical II
occurs under the action of the SiF3 group. The formaꢀ
tion of vinyl trifluorosilyl ether III is a thermodynamꢀ
ically favorable direction [17]; the traces of this ether
were detected in the mass spectra of reaction products.
It is likely that the occurrence of the reaction along
this path is hindered by kinetic barriers, and radical
It is likely that the reaction occurs by a similar
mechanism in the interaction of C2H3SiF3 with NO2
(Scheme 2). However, in this case, the trifluorosilyl
group, which is responsible for the direction of addiꢀ
tion, has a considerable effect. The quantumꢀchemiꢀ
cal calculations of the total atomization energy of reactions developed with the participation of biradical
optimized configurations demonstrated that the forꢀ
mation of ꢀradical rather than its isomer is more
favorable at the first step of addition. This effect is
explained by *ꢀp) conjugation between the antiꢀ
bonding orbital of the Si–C
II under conditions of an excess of NO2 lead to the forꢀ
α
I
β
(σ
H
.
π
O
F
F Si
F
F
O
σ
bond and the p orbital
C
F
Si CH + N
CH2
N+
with an unpaired electron of the
α
ꢀcarbon atom [16].
H
F
O−
O
H
I
O
O
H
O−
.
N+
H
O
H
H
H
H
H
.
F
F Si
F
F
F Si
F
O
N+
+
C
+ NO
C
O
O
N
.
.
C
H
C
H
O−
H
H
H
H
H
1
I
II
O−
.
O
H
F
F Si
F
N+
H
F
.
O
H
H
O
.
H
C
F Si
C
.
H
+ NO
H
H
.
H
C
F
C
H
H
H
H
H
II
III
1
2
Scheme 1. Mechanism of ethylene oxidation with
nitrogen dioxide proposed by Chao and Jaffe [11].
Scheme 2. Mechanism of the reaction of vinyltrifluoꢀ
rosilane with nitrogen dioxide.
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GASꢀPHASE OXIDATION OF VINYLTRIFLUOROSILANE WITH NITROGEN DIOXIDE
629
mation of final products, as described by Chao and
Jaffe [11]. The appearance of ethinyltrifluorosilane can
be explained by the elimination of a water molecule
from intermediate II. The formation of SiF4 can result
from deeper oxidation that leads to trifluorosilyl radiꢀ
cals [11]. The •SiF3 radicals tend to the disproportionꢀ
Transition
state
ation •SiF3 + •SiF3
SiF4 + SiF2. The formation of
N2O, NO, CO2, and H2O supports this hypothesis.
F3SiCHCH2NO2
48 kJ/mol
21 kJ/mol
The rateꢀlimiting step of the overall process is the
addition of NO2 to the C2H3SiF3 molecule to form
C2H3SiF3 + NO2
Fig. 4. Energy diagram for NO addition to C H SiF .
3
radical
energy profile of this step. The reaction rate constant
is = 3
10–14exp(–48000/RT cm3/s, as calculated
using the transition state theory.
I (Scheme 2). Figure 4 shows the calculated
2
2
3
k
×
)
model. The translational and rotational degrees of
freedom of all molecules are considered as an individꢀ
ual reservoir:
At room temperature,
10–22 cm3/s; this correꢀ
k
≈
sponds to a characteristic reaction time of about a day
under experimental conditions. Evidently, laser exciꢀ
tation considerably increases the rate of reaction.
However, several mechanisms of this acceleration can
occur.
dε
A
ꢀ
= σIA − k1Bε + k1Aε
A
B
dt
ε
A
A
A
ꢀ
− kVT(A + B)ε + kVTAε −
;
A
R
τ
KINETIC MODEL OF VIBRATIONAL
ENERGY CONVERSIONS
dε
dt
B
ꢀ
= k1Bε − kAε
A
B
Energy exchange processes are an integral part of
nonequilibrium reactions. Under conditions of a
highly disturbed Maxwell–Boltzmann distribution, a
kinetic consideration cannot be performed without
introducing relaxation equations [18]. Vibrational
energy conversion processes are of the greatest interꢀ
est. In the case of vibrationally excited polyatomic
molecules, there is a velocity distribution of various
processes [19]. The VV' exchange is most rapid; the
rate of this exchange can be higher by several orders of
magnitude than the rate of vibrational–translational
VT relaxation (henceforth, we consider an intramoꢀ
lecular equilibration). The difference between the
rates of VV' and VT relaxations allowed us to introduce
vibrational temperatures, which characterize the
energy content of individual sorts of molecules or even
individual vibrational modes (if intramolecular relaxꢀ
ation is hindered).
ε
B
B
B
ꢀ
− kVT(A + B)ε + kVTBε −
;
B
R
τ
dε
dt
= kVAT(A + B)ε + kVBT(A + B)ε
R
A
B
ε
A
VT
B
VT
R
ꢀ
ꢀ
− k A + k B ε −
.
(
)
R
τ
The term σIA corresponds to the laser pumping of the
system, and the last terms of the equations characterꢀ
ize energy dissipation due to heat transfer to reactor
walls.
A change to equations for the temperatures TA, TB,
and TR considerably simplifies the form of a set of
equations. For this purpose, we use the relationships
ε
=
cAATA
,
ε
=
cBBTB, and
ε
= cR(A + B)TR. In
B
R
To clarify the role of laser excitation in the accelerꢀ
ation of the test reaction, we used a simplified model
of vibrational energy conversion after a laser pulse.
The kinetic model does not pretend to quantitatively
describe the occurring processes; the aim of the kinetic
consideration is to predict the dependence of the rate
of reaction on the ratio between reactant concentraꢀ
tions or on the total pressure of the mixture.
addition, we introduce the relationships
A
A
B
B
, and
, which
kVTcA = kVTcR
k1cA = k1cB, kVTcR = kVTcR
follow from the equality of the rates of forward and
reverse reactions in an equilibrium. We obtain the folꢀ
lowing set of equations:
dTA
dt
σI
cA
=
− k B T −T
1 A B
(
)
For the test twoꢀcomponent system, we introduced
equations to describe the energy contents of the vibraꢀ
tional degrees of freedom of C2H3SiF3 and NO2 moleꢀ
cules. Table 2 summarizes the notation used in the
TA
)
− kVAT A + B T −T
)(
−
;
τ
(
A
R
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630
DEMENT’EV et al.
Table 2. Notation used in the kinetic model
ε
Bulk energy density in the vibrations of C2H3SiF3 (the energy is measured in laser radiation photons)
Vibrational heat capacity of C2H3SiF3 (measured in laser radiation photons per kelvin)
Vibrational temperature of C2H3SiF3
A
cA
TA
ε
Bulk energy density in the vibrations of NO2
B
cB
Vibrational heat capacity of NO2
TB
Vibrational temperature of NO2
ε
Bulk thermal energy density of translational and rotational motions of C2H3SiF3 and NO2 molecules
Bulk densities of C2H3SiF3 and NO2 particles, respectively
Laserꢀradiation absorption cross section
R
A, B
σ
I
Laserꢀradiation photon flux density
τ
Gas cooling time
˜
Constants of forward and reverse VV transfer between C2H3SiF3 and NO2, respectively
Forward and reverse VT relaxation constants of C2H3SiF3 molecules
k1
, k1
A
kVAT
,
,
kVT
˜
B
˜
kVBT
kVT
Forward and reverse VT relaxation constants of NO2 molecules
dTB
dt
c
cB
A k A T −T
⎧
⎨
⎛
⎞
cA A
t
=
(
)
1
A
B
TB = Tmax
exp
⎜
⎝
⎟
⎠
′
VV
c A + c B
⎩
τ
A
B
TB
)
τ
−kVBT A + B T −T
)(
−
;
t
⎛
⎞
cA A
cR(A + B)
(
B
R
(2)
(3)
+
exp −
⎜
⎟
⎠
cA A + cBBcA A + cBB + cR(A + B)
τ
⎝
VT
dTR
c
cR
=
A k A A T − T
(
)
⎫
⎬
⎭
cA A
VT
A
R
t
τ
+
exp − ;
dt
c
(
)
c A + c B + c (A + B)
A
B
R
TR
)
+
B kB B T − T
−
.
τ
(
VT
B
R
⎧
⎨
⎩
cA A
cR
TR = Tmax
c A + c B + c (A + B)
A
B
R
The temperatures TA
,
TB, and TR are measured with
reference to room temperature. We consider a laser
pulse to be very short. This results in the starting conꢀ
⎡
⎛
⎞⎤⎫
⎬
⎟
⎥
⎠⎦⎭
VT
t
t
× 1 − exp −
exp − .
τ
⎜
⎝
(
)
⎢
⎣
τ
E
cA A
ditions
and
, where E is
TB = TR = 0
TA = Tmax
=
The relaxation times are expressed in the following
the number of laser radiation photons absorbed in a manner:
unit volume. The solution can be found analytically
taking the VT relaxation constants to be equal:
c
1
= k1B + k A A + kVT A + B
;
(4)
(5)
(
)
τ
1 cB
A
B
.
kVT = kVT = kVT
VV'
The solution has the form
c A + B + c A + c B
(
)
1
R
A
B
.
= kVT
τ
cR
VT
⎧
⎨
⎛
⎞
cBB
t
TA = Tmax
exp
⎜
⎝
⎟
⎠
′
VV
Deriving the rate equations, we hypothesized that
the vibrational heat capacity is constant. Figure 5
shows the dependences of the vibrational energies of
C2H3SiF3 and NO2 on vibrational temperature, as calꢀ
culated in a harmonic approximation. As can be seen,
these dependences can be considered approximately
linear over a wide range of temperatures. The slope of
c A + c B
⎩
τ
A
B
cAA
cR(A + B)
(1)
+
cAA + cBBcAA + cBB + cR(A + B)
⎛
⎞
⎫
⎬
cAA
t
t
×exp −
+
exp − ;
τ
⎜
⎟
(
)
τ
c A + c B + c (A + B)
⎝
⎠
⎭
VT
A
B
R
KINETICS AND CATALYSIS Vol. 51
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2010

GASꢀPHASE OXIDATION OF VINYLTRIFLUOROSILANE WITH NITROGEN DIOXIDE
, K
631
T
E,
h
ν
25
20
15
10
5
1200
1000
800
c
R = 2.09
×
10−3 h
/K
ν
Ta
1
c
A = 11
×
10−3 h
/K
ν
600
Tb
400
Ttrans
c
B = 1.49
×
10−3 h
/K
ν
2
200
0
500
1000
1500
2000
, K
0
20 40 60
5000 10000 15000
Time,
T
μ
s
Fig. 6. Solution of the set of equations for vibrational temꢀ
peratures. The calculated values of the parameters , c ,
A B
c
Fig. 5. Temperature dependence of the vibrational energies
of ( ) vinyltrifluorosilane and ( ) nitrogen dioxide moleꢀ
cules. The numerical values of the heat capacities
and
c
and typical values of the parameters
A
and
B were
R
1
2
used. The pressures of C H SiF and NO were 40 and
2
3
3
2
c
,
c
,
200 Pa, respectively. The pulse energy corresponds to the
ν
A
B
and
c
are specified.
absorption of 10 per molecule of C H SiF .
h
R
2
3
3
the corresponding straight lies in Fig. 5 corresponds to step, which is characterized by different vibrational
the heat capacities cA and cB. Figure 5 also specifies the temperatures of mixture components. In this case, the
heat capacity cR, which results with consideration for reaction can be selectively stimulated and vibraꢀ
translational (3/2
freedom, in the units of
k
) and rotational (3/2
k
) degrees of tionally excited vinyltrifluorosilane molecules interact
h
ν
/K
.
with cold NO2 molecules even before the completion
of energy transfer processes. If the reaction occurs in
the course of the second or third step of relaxation,
selective reactions cannot be performed.
To illustrate the general pattern of relaxation proꢀ
cesses, Fig. 6 shows the vibrational temperatures TA
and TB and the translational–rotational reservoir temꢀ
perature calculated from the above equations as funcꢀ
tions of the elapsed time from the start of a laser pulse.
Typical concentrations of C2H3SiF3 and NO2 were
used. The laser beam energy corresponds to the
Dependence of the Rate of Reaction
on the Degree of Dilution
absorption of ten photons per molecule of C2H3SiF3
.
We determined the rate of reaction
decrease in the concentration of vinyltrifluorosilane
per pulse ( ):
γ
as the relative
The rate constants of VV' exchange and VT relaxation
were taken to be k1 =
1
×
10–11 and
k
VT = 3
10–13 cm3/s,
×
Δn
respectively.
Figure 6 clearly shows that there are three steps of
vibrational relaxation. The shortest first step characꢀ
terizes intermolecular VV' transfer, which occurs
immediately after the excitation of vinyltrifluorosilane
molecules. The VV' exchange comes into play during
the action of a laser pulse and lasts for a few microsecꢀ
onds. At the second step, the vibrational temperatures
of vinyltrifluorosilane and NO2 are the same; however,
the common vibrational temperature is strongly difꢀ
ferent from the translational temperature. At this step,
slower VT relaxation occurs. The thermal energy of
molecular motion increases. At the final step of the
process, the system reaches a complete equilibrium
and slowly cools to lose energy to the walls of a reacꢀ
tion cell. The characteristic time of cooling was a few
milliseconds under conditions of our experiments.
Bkeff
f
Δn
A
,
γ =
= Bk T ,T dt =
A B
∫
(
)
where
reaction, which depends on vibrational temperatures;
is the laser pulse repetition frequency; and
k(TA, TB) is the rate constant of a bimolecular
f
.
(6)
keff = f k T ,T dt
(
)
A
B
∫
Studying the dependence of the rate of reaction on
the degree of dilution of the mixture, we can deterꢀ
mine whether the reaction really occurs at the first
step, which is characterized by different vibrational
temperatures of mixture components. Indeed, for
mixtures with an excess of NO2, from Eqs. (1) and (4),
we obtain
In reactions initiated by laser radiation, it is of conꢀ
siderable importance at which step of vibrational
relaxation chemical reaction occurs. The most interꢀ
esting situation is that the reaction occurs at the first
⎛
⎞
1
t
t
and
.
≈ k A + B
(
)
TA = Tmax exp −
exp −
τ
1
⎜
⎝
⎟
⎠
(
)
τ
τ
VV '
′
VV
KINETICS AND CATALYSIS Vol. 51
No. 5
2010

632
DEMENT’EV et al.
К
×
1019, cm3/s
flux density of laser radiation. Thus, at a constant laser
eff
energy and a change in the total pressure of the mixꢀ
ture, the solution of a set of equations for vibrational
temperatures (Eqs. (1)–(3); Fig. 6) changes only as a
consequence of changes in the duration of individual
steps. A decrease in the concentration of vinyltrifluoꢀ
rosilane per pulse depends on total pressure as
1.2
1.0
0.8
0.6
0.4
0.2
0
Δn = kABτ ∝ P 2P −1 = P
,
VT
if the reaction occurs under conditions of a strong difꢀ
ference between vibrational and translational temperꢀ
atures, and
Δn = kABτ ∝ P 2P1 = P3
,
VT
1.0
1.2
1.4
1.6
1.8
[NO2]/[C2H3SiF3]
2.0
if the reaction occurs under conditions of equilibrium
heating.
Hence, it follows that a simple criterion allows us to
distinguish the roles of these steps in the test reaction:
if a chemical transformation occurs under conditions
of a strong difference of the vibrational temperature
from the translational one, the rate of a bimolecular
reaction is a linear function of pressure, W ~ P. If the
reaction occurs under full equilibrium conditions, the
Fig. 7. Dependence of the effective rate constant on the
ratio between reactants at a constant total pressure of
2
200 Pa. A laser with an energy of ~0.6 J/cm was tuned to
the R14 line.
The initial vibrational temperature of vinyltrifluoꢀ
rosilane molecules Tmax depends on the absorption
crossꢀsection and energy flux density of laser radiaꢀ
cubic relation is obeyed: W ~ P3
.
Note that the criterion proposed for the determinaꢀ
tion of the roles of various vibrational relaxation steps
is based on only the general concepts of relationships
between the rates of V–V' and V–T processes, and
particular values of vibrational relaxation rates are not
used in it.
tion. The duration of the first step
depends on
τ
VV '
only the constant of VV' transfer and the total concenꢀ
tration of particles in the irradiated volume. Thus, if
the laser pulse energy and the total concentration of
C2H3SiF3 and NO2 are kept constant, the time depenꢀ
dence of vibrational temperature TA remains
unchanged. Correspondingly, the effective rate conꢀ
stant found from Eq. (6) remains constant.
EXPERIMENTAL DEPENDENCE
OF THE RATE OF REACTION
ON THE DEGREE OF DILUTION
AND TOTAL PRESSURE
Dependence of the Rate of Reaction on the Total Pressure
The proposed criterion was applied to the test sysꢀ
tem. The energy density in a pulse and the laser generꢀ
ation frequency were kept constant; the reaction mixꢀ
tures contained an excess of nitrogen dioxide. To calꢀ
culate the effective relaxation time, the concentration
of vinyltrifluorosilane as a function of the number of
pulses was measured by mass spectrometry. The initial
portion of kinetic curves was approximated by a firstꢀ
The character of the dependence of the rate of
reaction on total pressure will answer the question of
whether the reaction occurs under conditions of
strongly different vibrational and translational temꢀ
peratures (second step in Fig. 6) or in full equilibrium
(third step in Fig. 6).
If the mixture composition is maintained constant
and the total pressure
time decreases: τVT
P
is increased, the VT relaxation
P
order equation with respect to C2H3SiF3
:
∼
1/ (Eq. (5)). The cooling time
of a gas mixture also depends on pressure; however, the
character of this dependence is essentially different.
Thermal relaxation is a diffusion process; therefore, an
.
A n = A exp −γn
( )
(
)
0
The effective rate constant was determined as
keff
= γ/B.
increase in the pressure results in an increase in
τ
. The
characteristic time of gas cooling in a cylindrical vessel
The observed secondꢀorder rate constant
decreased as the degree of dilution was increased
(Fig. 7). Therefore, the reaction occurs under condiꢀ
tions when the vibrational temperatures of both of the
components in the system were equalized. Under
these conditions, an increase in the degree of dilution
caused a decrease in the energy stored in the vibraꢀ
1
τ
5.78κ
of radius
R
is described by the equation
,
=
R2
where is the thermal diffusivity [20]. At a constant
κ
mixture composition, the thermal diffusivity is
inversely proportional to pressure; therefore, the coolꢀ
ing time is τ ∼ P.
The initial temperature Tmax of vinyltrifluorosilane tional reservoir and a decrease in the vibrational temꢀ
depends on the absorption crossꢀsection and energy peratures TA and TB
.
KINETICS AND CATALYSIS Vol. 51
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2010

GASꢀPHASE OXIDATION OF VINYLTRIFLUOROSILANE WITH NITROGEN DIOXIDE
633
To evaluate the orders of magnitude of TA, TB, and
lnw0
0
[
Pa/s]
Ttrans, we measured the amount of absorbed energy.
Under standard experimental conditions, absorption
weakly depended on reactant concentrations, and it
was about 20 photons of CO2 laser radiation per vinylꢀ
trifluorosilane molecule at an energy flux density of
0.56 J/cm2. Thus, the real temperature was somewhat
higher than that shown in Fig. 6.
−
−
−
−
2
4
6
We measured the dependence of the rate of reacꢀ
tion on the total pressure of reactants under conditions
of a twofold excess of NO2. The rate considerably
increased as the concentrations of reactants were
increased. The found numerical values of pseudoꢀ
firstꢀorder rate constants allowed us to calculate the
absolute initial rate and to determine the overall order
of reaction (Fig. 8), which was 2.7. This value is very
close to that expected on equilibrium heating.
8
3.0
3.5
4.0
4.5
5.0
5.5
6.0
lnp0
6.5
Pa
[
]
Fig. 8. Determination of the overall order of reaction from
the dependence of the logarithm of the initial reaction rate
Thus, the above kinetic analysis suggests that the
chemical reaction occurs with the participation of
excited molecules of both of the reactants. In this case,
the system occurs at the third step of vibrational
energy relaxation, that is, under conditions of a full
thermal equilibrium. It is likely that the acceleration of
reaction was due to the overcoming of an activation
barrier and it can be described by an Arrhenius equaꢀ
tion.
w
on the logarithm of the total pressure P of the reaction
0
0
mixture at the reactant concentration ratio
NO ]/[C H SiF ] = 2 : 1.
[
2
2
3
3
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KINETICS AND CATALYSIS Vol. 51
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2010