Kinetics of the reaction Al + SF6 in the temperature range 499-813 K

Article abstract of DOI:10.1021/jp012895n

Rate constants as a function of temperature for the reaction Al + SF₆ have been measured under pseudo-first-order conditions. Laser-induced fluorescence was used to monitor the relative concentrations of either the reactant Al or the primary pr

Full text of DOI:10.1021/jp012895n

J. Phys. Chem. A 2002, 106, 307-311
307
Kinetics of the Reaction Al + SF6 in the Temperature Range 499-813 K
James K. Parker, Nancy L. Garland, and H. H. Nelson*
Code 6110, Chemistry DiVision, NaVal Research Laboratory, 4555 OVerlook AVenue S.W.,
Washington, D.C. 20375
ReceiVed: July 26, 2001; In Final Form: October 4, 2001
6
Rate constants as a function of temperature for the reaction Al + SF have been measured under pseudo-
first-order conditions. Laser-induced fluorescence was used to monitor the relative concentrations of either
the reactant Al or the primary product AlF. The measured rate constants are described by the expression k(T)
-
10
3
-1 -1
)
6.8 (( 2.2) × 10 exp(-(4780 ( 200 K)/T) cm molecule
s
over the range 499-813 K. Ab initio
and density functional calculations at the MP2(FC) and BH&HLYP levels have been used to model the
potential energy surface for this reaction. Calculated rate constants are in good agreement with experimental
observations.
Introduction
yielded the bimolecular rate constant. Each first-order plot of
-
1
τ
vs PSF contained approximately 10 data points. Each data
6
Aluminum is used as a fuel in some solid rocket motors
because of its high energy density, its effect on suppressing
combustion instabilities, and because it is a relatively inexpen-
sive and readily available material.1 There are, however,
problems associated with using aluminum in the fuel. Al2O3(l)
slag can accumulate on the nozzle leading to a decrease in the
rocket’s overall performance, and it is also associated with the
formation of smoky exhaust trails. A potential solution to these
point on the first-order plot was obtained from a plot of LIF
intensity vs time, which contained 500 data points. When TMA
was the Al atom precursor, 2 laser shots per data point were
averaged; when TEA was the precursor, 8-10 laser shots per
data point were averaged. The total pressure in the reactor was
maintained at 100 Torr. In one experiment, AlF product
1
1
concentrations were monitored, by LIF on the A Σ T X Σ
transition near 227.5 nm, at varying partial pressures of SF6. In
this experiment, 10 laser shots per data point were averaged.
problems is to add fluorine-containing materials to the alumi-
nized propellant.2,3 It has been postulated that fluorine will
The stainless steel reactor consists of a 21-cm diameter,
double-hulled, spherical main body onto which four 20-cm
diameter vacuum flanges are welded. Cooling water flows
between the hulls through a series of baffles. The four ports on
the sides of the vacuum housing provide optical access for
collinear laser beams, for fluorescence collection at right angles,
and electrical access for resistive heating. The arms of the reactor
are sealed by flanges with copper gaskets. TMA/Ar, TEA/Ar,
Ar buffer gas, and SF6 gases were premixed in 6.4 mm stainless
steel tubing about 1 m upstream from the reactor; these gases
then flowed directly into the base of the reactor. Because TEA
has a low vapor pressure, it was necessary to bubble argon
through the liquid, which was heated to approximately 70 °C.
The gas lines were held at a temperature of approximately 120
°C with heating tape in order to prevent recondensation of the
TEA vapor. A three-way cross on the top of the reactor provides
ports for pumping, pressure, and temperature measurements. Gas
temperatures were measured with a 13%Pt/Rh thermocouple;
pressures were measured with a Baratron (MKS Instruments
627B13TBC1B). The thermocouple temperature was compared
with AlO rotational temperatures at 296 and 780 K. In both
cases, the temperatures determined by the two methods agreed
to within 5%.
eliminate formation of condensed phase metal oxide products,
shorten burn times of aluminum particulate, and enhance metal
ignition characteristics in oxygen environments by attacking the
aluminum oxide particle coating and lowering ignition temper-
3
ature. Mass spectrometric studies of the reaction of aluminum
and fluorine in oxygen/hydrogen flames have shown that major
product species in the flame are AlOF, AlOH, and AlO. In
systems where fluorine and oxygen are present, it has been
predicted that aluminum oxyfluoride (AlF2O) will be the
4
dominant final product. This species is a gas at rocket exhaust
temperatures.
In order for combustion modelers to have the ability to
accurately predict species distributions, a reliable kinetics
5
database is necessary. Currently, gas-phase kinetics data is
unavailable for reactions of aluminum with fluorinated com-
6
pounds, with the exception of NF3. In this investigation we
have undertaken a combined experimental and computational
study of the kinetics of the prototype reaction:
(1)
6
Al + SF f AlF + SF5
Results from this study will be used to guide further investiga-
tions in our laboratory.
A 5.7-cm o.d., 5.1-cm i.d., 30.5-cm long Al2O3 reaction tube
is situated inside the reactor. Four 1.3-cm holes in the middle
of the reaction tube, drilled 16.5-cm from the base, provide
optical access. The reaction tube is surrounded by a ceramic-
insulated resistor and Al2O3 insulation material. The resistor is
connected via vacuum electrical feedthroughs to a transformer
which provides current for heating.
Experimental Section
2
7
Al( P) atoms were generated by photolysis of trimethyl-
aluminum (TMA) or triethylaluminum (TEA) at 248 nm, and
2
were monitored by laser-induced fluorescence (LIF) via the S1/2
2
T P1/2 transition near 394.4 nm. A plot of the reciprocal Al
chemical lifetime (disappearance rate) vs SF6 partial pressure
1
0.1021/jp012895n CCC: $22.00 © 2002 American Chemical Society
Published on Web 12/15/2001

308 J. Phys. Chem. A, Vol. 106, No. 2, 2002
Parker et al.
The photolysis laser was a Lambda-Physik excimer laser
EMG 201 MSC) operating on KrF. The photolysis beam passed
reaction was measured at 20 Torr total pressure and 296 K.
-
13
3
-1 -1
(
Our value of 5.7 (( 0.5) × 10
cm molecule
s
is in
-
12
through a 6-mm diameter iris before being directed through the
MgF2 windows of the reactor. The Al chemical lifetime had no
dependence on the photolysis pulse energy which varied from
excellent agreement with the value of 0.60 ((0.05) × 10
3
-1 -1
9
cm molecule
s
reported by Garland et al. at 20 Torr and
298 K. The Ga + SF6 rate constant was measured at 100 Torr
-
1
2
-14
3
-1
2
0 to 60 mJ pulse . The Al( P) atoms were probed with the
output of a Lambda-Physik excimer pumped dye laser (EMG
02/FL2002) operating with PBBO dye in dioxane. The dye
and 296 K. Our value of 1.4 (( 0.2) × 10
cm molecule
-
1
s
compares reasonably well with the literature value of
-
15
3
-1 -1
1
8 (( 3) × 10
cm molecule s .
laser and photolysis laser beams were collinear and counter-
propagated through the reactor. The fluorescence was focused
by a two-lens telescope through an iris onto a filtered photo-
multiplier tube (PMT) (Burle C31000M). A Corning 5-58 band-
Computational Methods
The ab initio and density functional calculations were carried
2
10
pass filter, which transmitted fluorescence of the Al( S1/2) T
out via the Gaussian 98 suite of programs running on a Silicon
2
Al ( P1/2) transition, was used as well as a 1-cm thick quartz
Graphics Origin 2000 computer. Geometry optimizations and
calculation of normal, harmonic vibrational modes for reactants,
products, and transition state structures, were carried out at the
BH&HLYP/6-31G(d), BH&HLYP/6-311++G(2d), MP2(FC)/
6-31G(d), and MP2(FC)/6-311++G(2d) levels of theory.1
Single-point energies were computed using the aug-cc-pVTZ
cell of CCl4 to block scattered photolysis laser light from the
photomultiplier tube. For the AlF experiment, a 228 nm band-
1
1
pass filter was used to transmit fluorescence of the A Σ T X Σ
transition near 227.5 nm. In this case, 455 nm laser radiation
was passed through a BBO doubling crystal to generate photons
at 227.5 nm. The output power at this wavelength was
1-17
1
8
basis set for all stationary points at the BH&HLYP/6-
311++G(2d) and MP2(FC)/6-311++G(2d) levels of theory.
The unrestricted MP2 method was used on species with doublet
spin multiplicity. Accordingly, all MP2 relative energies in this
paper have been determined utilizing the UMP2 electronic
potential energies. For calculations on species with doublet spin
-
1
approximately 150 µJ pulse .
A programmable digital delay generator (DDG) (SRS DG-
35) controlled the timing for the kinetics experiments. The
5
DDG provides trigger pulses at a fixed delay to the photolysis
laser and at variable delays simultaneously to the probe laser
and the boxcar integrator. A gated boxcar integrator captured
the LIF signal and directed it to a computer. The Al and AlF
chemical lifetimes were obtained by sequentially increasing the
delay between the two laser pulses. All kinetics scans were
initiated 5 µs after the photolysis laser trigger to ensure that
2
multiplicity, the value of 〈S 〉 prior to annihilation is less than
0
.77, indicating that these species are well-described by a single
1
9
determinant wave function.
2
0,21
Canonical transition state theory
was used to predict rate
constants for these reactions within the temperature range studied
by experiment. The rate constants, k(T), were computed with
the following expression:
2
1
the Al( P) and AlF X Σ would be in thermal equilibrium with
the bath gas.
The flow rates of the gases were measured with calibrated
mass flow meters (Tylan 2950). For kinetics experiments at 100
Torr and in the temperature range of 499 to 612 K, 500 standard
cubic centimeters per minute (sccm) of argon and 30 sccm of
TS
k T
-∆Ea
b
Q
k(T) )
exp
(2)
Al SF
(
)
h Q Q
k T
6
b
0.1% TMA in Ar were flowed through the inlet tube. A flow
Here Q , Q , and QSF6 are the total computed partition
TS
Al
of 100 sccm of Ar was directed over the windows to prevent
accumulation of metallic aluminum. Above 600 K the aluminum
LIF signal strongly decreased to zero in the presence of sulfur
hexafluoride. Quenching was ruled out as the cause of signal
loss because simply turning off the SF6 flow did not restore the
aluminum LIF signal after several turnovers of gas in the cell.
The use of TEA from 638 to 813 K and much faster flow rates
partially alleviated this problem. However, an upper limit of
functions (including rotational symmetry numbers, where ap-
propriate) for the transition state, Al atom, and SF6 molecule at
temperature T, ∆Ea is the activation energy including zero-point
vibrational correction and thermal corrections to the enthalpy,
kb is Boltzmann’s constant, and h is Plank’s constant. In
computing the electronic function for the aluminum atom, the
2
2
22
multiplicity of the states P3/2 and P1/2 and the energy gap of
-1
1
12.06 cm have been taken into consideration.
8
13 K on the temperature was reached due to difficulty
maintaining Al LIF signal in the presence of SF6. When TEA
was used, 5.0 standard liters per minute (slpm) of Ar buffer
gas and 40 sccm of approximately 0.25% TEA in Ar were
flowed through the inlet tube. A flow rate of 100 sccm of argon
was maintained over the windows. As SF6 was added to the
system, the partial pressure of the Ar buffer gas was decreased
to maintain the total pressure. All kinetics experiments were
carried out under pseudo-first-order conditions. Sulfur hexafluo-
ride concentrations were greater than 100 times the concentration
of either Al or AlF, ensuring pseudo-first-order conditions.
Results
2
Figure 1 shows typical temporal decay profiles for Al( P)
LIF signal generated using TMA and TEA precursors. The
signal-to-noise ratio in experiments where TMA was used as
the Al atom precursor is much higher than for those experiments
involving TEA. Consequently, the number of laser shots per
data point was increased from 2 in the TMA experiments to
8
-10 in the TEA experiments. The main factors contributing
to the aluminum atom disappearance rate in the absence of added
TMA and TEA were obtained from Akzo Nobel (95% pure,
other impurities consisted of higher molecular weight aluminum
alkyls). TMA was subjected to several freeze-pump-thaw
cycles before use in order to remove volatile impurities such
as methane. Ar (Air Products, 99.995%), and SF6 (Matheson,
SF are reaction with unphotolyzed TMA and diffusion. The
6
23
reaction rate constant of Al + TMA at 296 K is reported to
-
10
3
-1 -1
be 1.3 ((0.3) × 10
cm molecule s . We also measured
-
10
3
-1 -1
a value of 1.3 (( 0.1) × 10 cm molecule
s
for this rate
constant at 296 K using the same assumptions (i.e., dimerization
of TMA neglected) as the investigators of ref 23. At room
temperature, all Al LIF decay curves were single exponential.
At higher temperatures, in the absence of SF6, biexponential
9
9.995%) were used without further purification. The system
was calibrated against known rate constants from the Al + CO2
and Ga + SF6 reactions.8,9 The rate constant for the Al + CO2

Kinetics of the Reaction Al + SF6
J. Phys. Chem. A, Vol. 106, No. 2, 2002 309
Figure 2. Linear dependence of 1/τ for Al atom decay as a function
of SF partial pressure at different temperatures. Ptot ) 100 Torr.
6
Second-order rate constants are obtained from the slopes.
Figure 1. A: Typical Al atom decay profile when TMA was the
photolytic precursor. B: Typical Al atom decay profile when TEA was
the photolytic precursor. Solid lines through the data are double
exponential fits.
Figure 3. Kinetic behavior of AlF LIF signal over time. Solid line
through the data is a double exponential fit using eq 2. PSF6 ) 875
mTorr, Ptot ) 100.5 Torr, and T ) 594 K.
TABLE 1: Summary of Rate Coefficient Measurements for
Al + SF
6
f AlF + SF
5
k (10- cm
13
3
k (10-13 cm
3
molecule s-1
-
1
molecule s-1
-1
the slope of each pseudo-first-order plot increases with increas-
ing temperature.
T (K)
)
T (K)
)
499
518
556
573
594
612
638
0.42
0.61
1.3
666
693
721
723
747
771
813
4.9
6.7
8.6
The rate constant at 594 K was measured by following
formation and decay of the primary product AlF. A typical time-
dependent profile for formation and decay of AlF LIF signal is
shown in Figure 3. In our experiment, there were significant
sources of AlF product independent of SF6. The AlF profiles
analyzed were the difference between profiles collected with
and without added SF6. For a set of coupled reactions of the
form:
2.1
3.9
6.9
a
13.0
14.2
23.8
3.3
3.7
a
Obtained by monitoring relative concentrations of AlF.
decay was observed and attributed to the equilibrium process:
Al + SF f AlF + SF
(1)
(3)
6
5
Al + TMA T Al[TMA].
AlF f removal
At still higher temperatures (T > 425 K), equilibrium is
established prior to our first observation and single-exponential
decay is again observed with the long decay constant. Under
these conditions, when SF6 is added to the system, the decay is
biexponential. The short time constant is due to reaction of free
Al with SF6, whereas the longer time constant results from the
equilibrium of Al with TMA or TEA. The details of this aspect
of the Al atom reaction with trialkylaluminum will be addressed
in a future publication.
Table 1 lists the measured values of the bimolecular rate
constants for the Al + SF6 reaction obtained in this work.
Thirteen of these rate constants were measured by following
the disappearance of Al LIF signal while varying the partial
pressure of SF6. The individual decay times measured at three
of the temperatures are plotted as a function of SF6 pressure in
Figure 2. As expected for a bimolecular reaction with a barrier,
it can be shown24 that
[
Al]0k
1
[AlF] )
(4)
k3 - k1
where [Al]0 is the concentration of aluminum atoms at t ) 0,
k1 is the pseudo-first-order rate constant for reaction of Al with
SF6, and k3 is a pseudo-first-order rate constant for removal of
AlF. Reaction 3 represents disappearance of AlF by reaction
with SF6, aluminum atom precursor, and diffusion out of the
viewing region.
By fitting the AlF formation and decay data to the double
exponential expression of eq 4, the pseudo-first-order rate
constants for formation and decay of AlF at eleven different
partial pressures of SF6 were determined. The range of SF6

310 J. Phys. Chem. A, Vol. 106, No. 2, 2002
Parker et al.
TABLE 2: Reaction Enthalpies, Activation Energies, and Arrhenius Preexponential Factors Calculated for the Reaction Al +
SF
6
f AlF + SF
5
at Various Levels of Theory
(kcal mol-1)
E
(kcal mol-1
)
A (10-10 cm molecule s-1
3
-1
)
level of theory
∆
r
H
0
a
MP2/6-31G(d)
MP2/6-311++G(2d)
MP2/aug-cc-pVTZ//MP2/6-311++G(2d)
BH&HLYP/6-31G(d)
BH&HLYP/6-311++G(2d)
BH&HLYP/aug-cc-pVTZ//BH&HLYP/6-311++G(2d)
exptl
-56.2
11.1
10.8
13.2
10.1
9.5
12.3
9.5 ( 0.4
0.81
2.2
2.2
1.4
1.2
1.3
6.8 ( 2.2
-63.1
-57.7
-58.3
-64.8
-60.7
-68.0 ( 3.8a
a
From ref 22.
Figure 6. Calculated geometrical parameters of the Al + SF
6
atom-
abstraction transition state. The molecular symmetry point group is C4V
.
Figure 4. Linear dependence of 1/τ for AlF formation as a function
of SF partial pressure. Ptot ) 100 Torr.
plot were determined by adding in quadrature the independent
experimental errors (assumed to be 5% for gas flow rate, 5%
for temperature, 5% for pressure, and 2% for timing) and the
statistical error from the pseudo-first-order plots.
6
Discussion
First, it is noted that the preexponential factor for reaction 1
2
5
is typical for atomic metatheses reactions. The only other
experimentally measured rate constants for the reaction of
aluminum with a fluorinated species in the gas phase are those
1
9
for the Al + NF3 f AlF + NF2 reaction. For this reaction,
-
10
exp(-(2990 ( 100 K)/T) cm3
over the temperature range 300-800 K. The
barrier height of 2990 K corresponds to an activation energy
k(T) ) 2.1 (( 0.4) × 10
-
1
-1
molecule
s
-
1
of 5.9 kcal mol . This is a reasonable activation energy and
preexponential factor for an atom abstraction reaction and places
our results for the Al + SF6 reaction in context. Interestingly,
the authors of the Al + NF3 work were not able to get reliable
kinetic information above 800 K due to decomposition of NF3
on the walls of the reactor. As mentioned above, we had similar
problems in this study.
6
Figure 5. Arrhenius plot for Al + SF . The solid curve through the
-
10
data represents k(T) ) 6.8 (( 2.2) × 10 exp(-(4780 ( 200 K)/T)
3
-1 -1
cm molecule
s . Circles represent data from Al atom decays; triangle
represents data from AlF formation kinetics.
We have computed the potential energy surface of this
reaction using second-order perturbation theory with the frozen
core approximation, MP2(FC), and the BH&HLYP density
functional method, both with various basis sets. The BH&HLYP
functional was chosen because of its known reliability in
calculating barrier heights for some reactions involving fluo-
partial pressure was from 0.87 to 11 Torr. A plot of the
formation rate constant as a function of partial pressure of SF6
yielded the bimolecular rate constant for reaction 1 at 594 K.
This plot is shown in Figure 4. The resulting rate constant is in
reasonable agreement with the rate constants obtained by
monitoring Al atom decay, demonstrating that AlF is a primary
product of this reaction.
26
rine. We also attempted to use the more popular B3LYP
functional, but a transition structure could not be located. All
calculational methods for which a TS was obtained find an atom
abstraction transition structure with an S-F-Al collinear bond
angle. Figure 6 gives geometrical parameters of the transition
state calculated at the four levels of theory. There is general
agreement on the structure of the TS among the four methods
used.
The results of the ab initio and DFT calculations have been
used to calculate bimolecular rate constants at 500, 600, 700,
and 800 K using eq 2. For each set of calculated rate constants,
The bimolecular rate constants of reaction 1 as determined
from Al disappearance are plotted in Arrhenius form in Figure
-
10
5
. Regression analysis yielded k(T) ) 6.8 (( 2.2) × 10
-
3
-1 -1
exp(-(4780 ( 200 K)/T) cm molecule s . This corresponds
to an activation energy of 9.5 ( 0.4 kcal mol . Weighting
factors of (uncertainty in k) were used in the fit. Also shown
in Figure 5 is the rate constant determined from AlF appearance
data. Errors in the measured rate constants on the Arrhenius
-
1
-
2

Kinetics of the Reaction Al + SF6
J. Phys. Chem. A, Vol. 106, No. 2, 2002 311
Arrhenius parameters were extracted. A summary of the thermo-
kinetic computational results is provided in Table 2. The
calculated structural and vibrational information for reactants,
products, and the transition state of this reaction are available
as Supporting Information. From Table 2 we find that the
BH&HLYP/6-311++G(2d) method gives the best agreement
with experiment for predicting the enthalpy of reaction and the
activation energy over the experimental temperature range. In
both cases, this method yields calculated parameters which are
within the stated experimental uncertainty. Increasing the basis
set to aug-cc-pVTZ for both BH&HLYP and MP2 methods,
using single point energies from structures optimized in the
Supporting Information Available: Structural and vibra-
tional information for reactants, products, and the transition state
of the Al + SF6 f AlF + SF5 reaction from the ab initio and
DFT calculations. This material is available free of charge via
the Internet at http://pubs.acs.org.
References and Notes
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New York, 1992.
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Compositions for Ramjet Fuels. Presented at the 8th International Sympo-
sium on Air Breathing Engines, Cincinnati, OH, June 14-19, 1987.
(
3) Yetter, R. A.; Dryer, F. L.; Rabitz, H.; Brown, R. C., Kolb, C. E.
Combust. Flame 1997, 112, 389.
4) Farber, M.; Srivastava, R. D. Combust. Flame 1976, 27, 99.
6
-311++G(2d,p) basis set, moves the activation energy up (and
-
1
away from the experimental value) by 2.8 and 2.4 kcal mol ,
respectively. Also, the computed enthalpies of reaction at the
BH&HLYP/6-311++G(2d) and MP2/6-311++G(2d) levels of
theory move up and out of the range of experimental uncertainty
when the aug-cc-pVTZ basis set is used. These trends, which
are independent of correlation method, suggest that reoptimi-
zation of structures may be important when moving to the aug-
cc-pVTZ basis set. We attempted to optimize the transition state
structure from the BH&HLYP/6-311++G(2d,p) level at the
BH&HLYP/aug-cc-pVTZ level of theory but the calculation
failed due to our lack of computational resources.
(
(5) Ernst, L. F.; Dryer, F. L.; Yetter, R. A.; Parr, T.; Hanson-Parr, D.
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(
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The MP2/6-311++G(2d) method gives an Arrhenius pre-
exponential factor in closest agreement with experiment.
However, all methods underestimate the A-factor for this
reaction. The simplest explanation for the small calculated
A-factors is that the calculated transition structure is too “tight”.
A looser transition state would mean a longer Al‚‚‚S distance,
which would lead to an increase in the moments of inertia of
the TS. This would increase the value of the rotational partition
function. Also, a looser TS would tend to decrease the values
of the lowest lying vibrational mode (bending mode, E sym-
metry), causing the vibrational partition function of the TS to
increase, thereby increasing the A-factor.
98, Revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998.
(
(
11) Lee, C.; Yang, W.; Parr, R. G. Phys ReV. B 1988, 37, 785.
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7
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265.
(
(
Summary
1
The rate constants of the reaction of Al + SF6 were measured
between 499 and 813 K at 100 Torr total pressure. The reaction
proceeds through an atom abstraction transition state with an
(
3
(
(
18) Dunning, T. H. J. Chem. Phys. 1989, 90, 1007.
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Acknowledgment. We thank A. P. Baronavski and T.
Russell for helpful discussions. We also thank A. D. Berry for
help in handling and transfer of aluminum alkyl reagents, and
H. D. Ladouceur for help in reactor design. This work was
supported by the Office of Naval Research through the Naval
Research Laboratory and was performed while J. K. Parker held
a National Research CouncilsNaval Research Laboratory
Associateship.
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