Ion-molecule kinetics at 15-700 Torr

Article abstract of DOI:10.1039/b417454b

Studies of ion-molecule chemistry are usually made at pressures of a few Torr and below. By contrast, there are numerous plasmas that occur at higher pressures. For that reason we have constructed a turbulent ion flow tube (TIFT) for studying ion-molecule kinetics from 15 to 700 Torr. Currently, the TIFT operates from room temperature to 700 K. Here we present a summary of the measurements we have made to date. The first measurements involved SF ₆^- reactions with SO₂, H₂O, CH ₃OH and C₂H₅OH at room temperature. The SO ₂ reaction showed the same kinetics as low pressure measurements indicating that the reaction occurs rapidly. The other reactions were all found to be cluster-mediated with branching fractions that depend on pressure. More recently, charge transfer reactions of O₂⁺ to alkylbenzenes have been studied at elevated temperatures, from 400 to 700 K. Both dissociative and non-dissociative charge transfer occurs with the latter being favored at high pressures indicating that excited states live long enough to be stabilized by the buffer gas. Combining the TIFT measurements with detailed statistical adiabatic channel model/classical trajectory (SACM/CT) calculations of the unimolecular decay constant allows energy transfer parameters to be derived. Extending the temperature range upwards to 750 K has allowed thermal decomposition rate constants to be measured. The thermal decomposition has been successfully modeled using the same parameters as for the collision quenching modeling. This allows bond strengths for the dissociation to be derived with high accuracy. Both the measurements and models show that the conditions correspond to the high pressure kinetics regime. The Owner Societies 2005.

Full text of DOI:10.1039/b417454b

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R E S E A R C H P A P E R
Ion–molecule kinetics at 15–700 Torrw
a
A. A. Viggiano,a Abel I. Fernandezz and J. Troe*b
a Air Force Research Laboratory, Space Vehicles Directorate, 29 Randolph Rd., Hanscom
Air Force Base, MA 01731-3010, USA
b Institut fur Physikalische Chemie, Universitat Gottingen, Tammannstrasse 6,
D-37077 Gottingen, Germany. E-mail: shoff@gwdg.de
¨
¨
¨
¨
Received 16th November 2004, Accepted 24th January 2005
First published as an Advance Article on the web 9th February 2005
Studies of ion–molecule chemistry are usually made at pressures of a few Torr and below. By contrast, there are
numerous plasmas that occur at higher pressures. For that reason we have constructed a turbulent ion flow tube
(TIFT) for studying ion–molecule kinetics from 15 to 700 Torr. Currently, the TIFT operates from room
temperature to 700 K. Hereꢀwe present a summary of the measurements we have made to date. The first
measurements involved SF6 reactions with SO2, H2O, CH3OH and C2H5OH at room temperature. The SO2
reaction showed the same kinetics as low pressure measurements indicating that the reaction occurs rapidly.
The other reactions were all found to be cluster-mediated with branching fractions that depend on pressure.
1
More recently, charge transfer reactions of O2 to alkylbenzenes have been studied at elevated temperatures,
from 400 to 700 K. Both dissociative and non-dissociative charge transfer occurs with the latter being favored at
high pressures indicating that excited states live long enough to be stabilized by the buffer gas. Combining the
TIFT measurements with detailed statistical adiabatic channel model/classical trajectory (SACM/CT) calculations
of the unimolecular decay constant allows energy transfer parameters to be derived. Extending the temperature
range upwards to 750 K has allowed thermal decomposition rate constants to be measured. The thermal
decomposition has been successfully modeled using the same parameters as for the collision quenching modeling.
This allows bond strengths for the dissociation to be derived with high accuracy. Both the measurements and
models show that the conditions correspond to the high pressure kinetics regime.
excellent platform for such studies. Seeley et al.7 developed a
turbulent ion flow tube for neutral studies. Since ions are lost
on every collision with walls, and this instrument had minimal
Introduction
High pressure ion–molecule reactivity studies have tradition-
ally been limited to less than 5 Torr. Only occasionally have
wall losses, the adaptation to ion studies seemed straight-
studies been made above this range. In 1996, Knighton and
forward and practical. With all the above in mind, our group
at the Air Force Research Laboratory (AFRL) developed such
an instrument. So far, studies have been made from 15–700
Torr and from 300–700 K. This paper reviews the development
have been published since. The need for such data is obvious
of the instrument and all the studies performed to date.
since many plasmas occur at or near atmospheric pressure.
Grimsrud1 summarized all studies in what they termed the
‘‘very high pressure’’ (VHP) regime, i.e. from 0.01 to 10 atm.
At that time, they found less than 20 VHP papers and few more
Examples include the Earth’s atmosphere,2,3 plasma assisted
combustion,4 and plasmas around fast moving vehicles in the
Experimental
lower atmosphere.5,6 In addition, a number of analytical
The AFRL turbulent ion flow tube (TIFT) is based on the
instrument designed by Seeley et al. for neutral kinetics.7 The
instruments involve VHP plasmas including atmospheric pres-
sure mass spectrometers, ion mobility spectrometers, and
electron capture detectors in gas chromatographs.
current version of the instrument is shown in Fig. 1. The
instrument has gone through moderate changes since the first
version,8 mainly to introduce temperature variability. In many
ways, the TIFT operates similarly to low pressure flow tubes
used for ion–molecule reaction studies9 and indeed the same
software controls both the low and high pressure apparatuses
in our laboratory.10,11 In all ion flow tubes, ions are created,
carried down an approximately one metre tube by a large
carrier gas flow, and sampled into a mass spectrometer.
Neutral reagents are added at various intermediary points.
The main difference between the low and high pressure instru-
ments is that the TIFT uses larger buffer gas flow rates which
results in turbulent instead of laminar flow. Turbulent flow is
obtained for Reynolds numbers greater than 3000.12
The buffer enters the flow tube through a sidearm as shown
in Fig. 1. Typical flow rates are 40–80 standard litre per minute
(slm), which makes N2 taken from liquid as the most practical
and economic choice. Note that a 1A cylinder of gas lasts only
about an hour and needs to be trapped to rid the gas of
impurities. While this is possible, it is expensive and requires
It is well known that pressure can quench certain species and
affect the yield of products. For this to occur, the time between
collisions of the buffer gas and the intermediate species must be
less than or on the order of the lifetime of the intermediate
state. At atmospheric pressure, typical collision times are
on the order of 10ꢀ10 s. Since ion–molecule reactions often
involve long lived complexes, many reactions may have inter-
mediates that live long enough to encounter a collision with the
buffer gas.
Several techniques have been used to make measurements in
the VHP regime. These have been summarized in the review of
Grimsrud and Knighton.1 They pointed out that flow tubes
had never been used for such studies but that they should be an
w Presented at the Bunsen Discussion on Chemical Processes of Ions,
Marburg, 15–17 September 2004.
z Abel I. Fernandez, is a National Academy of Sciences Postdoctoral
Fellow.
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5
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Fig. 2 Schematic of the neutral injector design with turbulizers
attached.
Fig. 1 Schematic view of the variable temperature turbulent ion flow
tube (TIFT).
reduced the mixing time. The turbulizers and showerhead were
added one at a time and all three were needed to reduce the
effective mixing distance to less than approximately one cm.
A thin thermocouple is placed at the end of the moveable tube
to measure the gas temperature.
The flow tube is heated in four zones. The three outside the
sampling region are broken up into two relatively short end
zones and a long central one. All use jacket heaters with built in
thermocouples. Additional inlets are incorporated for adding
gases or measuring the ion velocity. The pressure is controlled
by a MKS control valve. The inside zone is heated by ceramic
coated wire.
The gas is sampled through a truncated nose cone with a
50–150 micron orifice. The ensuing supersonic beam is
skimmed and sampled into a quadrupole mass spectrometer.
The ions are detected by a discrete dynode particle detector.
Both the nose cone and skimmer are isolated and voltages are
applied.
In order to measure accurate rate constants, the ion velocity
must be known since it is well known that ion velocities are
greater than the bulk flow velocity.9 In laminar flow the profile
of the neutral velocities is parabolic, with the centerline
velocity being twice the average. The ion profile is peaked on
the central axis since at the boundary ions are lost to the walls
with almost complete efficiency. When ions are sampled from
the center, the average velocity is typically around to 1.6 times
the average due to diffusion. In turbulent flow, the neutral
velocity profile is closer to being square shaped and the center-
line velocity is much closer to the average velocity. In order to
accurately account for this, it is best to measure the ion
velocity. We have done this in the TIFT by pulsing thin wires
at two distances from the nose cone and looking for the time at
which the ion disturbance reached the detector. The ratio of
ion velocity to buffer velocity was found to vary from E2 for
the peak neutral velocity at low Reynolds numbers to E1 at
very high Reynolds numbers.8 Under typical operating condi-
tions, the ratio is about 1.1 to 1.2. No dependence on pressure
was found.
By measuring the ion velocity, the mixing distance, as well as
all the normal flow tube parameters such as pressure, tempera-
ture and flow rates, the error for this instrument is believed to
be similar to that for other fast flow apparatuses. The error
limits are quoted as ꢁ15% relative error and ꢁ25% absolute
error. At present we have made measurements from 15–700
Torr. Below about 25 Torr, it is not possible to run in the
turbulent flow regime since the pump is not fast enough. Rate
constants are more difficult to measure at the low pressures but
branching ratios are not as problematic since they rely only on
the relative signals of two or more ions. At present we have
made measurements from 300 to 700 K and have plans to
increase this upper temperature limit by 100–200 K.
much attention. The large flow rate requires the gas to be
preheated since wall collisions in the flow tube are not sufficient
for the gas to come into equilibrium with the wall tempera-
ture.13 The current design has the gas flowing through a
stainless steel rod with star shaped flow channels being cut
into it as shown in the insert in Fig. 1. The tube is heated by
cylindrical clamshell heaters. The temperature of the gas exit-
ing the heater is regulated to the flow tube temperature as
measured by a thermocouple at the end of the reactant inlet. It
is necessary to overheat the gas by about 100 1C to compensate
for heat losses in the upstream end of the apparatus and for
introduction of unheated source gas.
A corona discharge ion source (coaxial cylinder geometry)
creates ions in the sidearm. The corona is separated from the
main flow by a cup with a 1 mm exit hole. This allows the
corona to run at relatively high pressure even when the flow
tube is operated at 15 Torr. The corona so far has been used to
make only O21. The first experiments used pure O2 in the
corona, although it was recently found that a mixture of
mainly Ar (E1 slm) with a small amount of O2 (E3 standard
cubic centimetres per minute, sccm) yields a stronger ion signal
at low pressure. The Ar/O2 combination also greatly reduces
the amount of [O2] needed (E1% of the pure O2 case) which
reduces interference from neutral O2 in the study of some slow
reactions. Higher Ar flows are found to be necessary at high
pressure to prevent backstreaming. In order to reduce water,
the corona gases are passed through a molecular sieve trap at
approximately ꢀ100 1C (methanol slush bath). The voltage on
the corona varies with condition from 1000–5000 V, typically
2000 V. The position of corona needle can be adjusted and the
tip is typically less than 1 cm upstream of the orifice. The cup
periodically needs to be sanded to rid it of an unwanted
oxidation layer which causes ion signal degradation. The side-
arm, except for the corona holder, is heated to the flow tube
temperature by a heating jacket. The first studies involving
ꢀ
SF6 used a Po-210 radioactive ion source instead of the
corona at room temperature only. Experiments at elevated
temperatures require preheating of the gas (see above) but
because the Po foil would melt, it was necessary to switch to the
corona source. Other sources have not been explored at this
time.
The heated gas enters the flow tube and is carried past a
neutral injector where the reactant neutral is added. Rate
constants and branching ratios are typically measured by fixing
the distance and varying the reagent flow rate. A flush gas co-
flows with the reagent to reduce the effective volume of the
injector. This proved important for operation at pressures
approaching 100 Torr and above to reduce settling time. The
injector distance can be changed and the kinetic measurements
repeated. This allows mixing times to be estimated. With a
truncated straight tube as the inlet, exceedingly long mixing
times were found. To circumvent this, two fan blades and a
showerhead were added to create small local eddies which
promote turbulent flow and enhance mixing. The injector with
these additions is shown in Fig. 2. The additions greatly
Frequently, impurities have been a problem, particularly
water vapor. This requires baking of the instrument and inlet
lines as well as trapping of the corona gases and He when it has
been used as a buffer. This has limited operation to ions that do
not react with H2O or an oxygen impurity in the N2 buffer. At
room temperature, SF6ꢀ was made quite cleanly. Above 423 K,
1
O2 can be made cleanly. Below this temperature, oxygen
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large pressure dependences. The reaction had been studied
previously15,16 and three product ions were known to be
formed,
ꢀ
ꢀ
SF6ꢀ þ SO2 - SF5 þ FSO2
ꢀ
SF6ꢀ þ SO2 - FSO2 þ SF5
ꢀ
SF6 þ SO2 - F2SO2 þ SF4.
(1)
In this work and in the previous studies only the charged
species were observed; thus, the neutral products given above
ꢀ
are presumed to exist. Since SF6 does not react with any
common impurities, both rate constants and products ratios
could be studied. Because this reaction is not expected to have
a pressure dependence and because the rate constants, 1.0 ꢂ
10ꢀ9 cm3 sꢀ1 over the entire pressure range, are in good
agreement with previous low pressure measurements, these
results showed that the TIFT can be used to make accurate
kinetic measurements over the wide pressure range. The pro-
duct distribution was also found to be invariant and consistent
with the low pressure measurements. The average values are
24, 60 and 16% for SF5ꢀ, F2SO2ꢀ, and FSO2ꢀ, respectively.
The lack of a pressure dependence in either the branching ratio
or rate constant indicates that the lifetime of an SF6ꢀ–SO2
complex is shorter than the lifetime with respect to collisions
with the N2 buffer gas, which is 70 ꢀps at 700 Torr.
Fig. 3 Low-resolution mass spectra with and without ethylbenzene
.
1
reagent in the study of O2 with C8H10
clusters rapidly to water and then forms H3O1(H2O)n ions.14
These impurities frequently limit the highest pressure at which
branching fractions can be measured. When reporting branch-
ing ratios, ionic impurities are limited to less than 3%; this is
needed to avoid falsification of the branching ratio measure-
ments by parallel/competitive reactions. A typical spectrum
1
with O2 as the primary ion and with and without neutral
A study of the reactivity of SF6 with H2O, CH3OH and
C2H5OH from 50 to 500 Torr at 298 K proved more interest-
ing.17 The first reaction is important in electrical discharges
when SF6 is used as a high voltage gaseous dielectric. Studies of
all three reactions showed the decline of the SF6ꢀ parent to be
second order in the solvent. The mechanism, shown for water
vapor, is
ethylbenzene reagent gas is shown in Fig. 3. Without reagent,
there are less than one percent impurity ions. Presently we can
do even better (by reducing small leaks and more baking). The
exception is non-reactive alkali ions, e.g., Na1, K1, that are
emitted from surfaces at high temperatures. Note that the
spectra in Fig. 3 were taken under low resolution conditions
to minimize mass discrimination since it is not possible to
quantify mass discrimination in this instrument. Our experi-
ence indicates that the low resolution spectra have little
discrimination since ion balance is good. In order to account
for ionic species separated by one or two masses, the low
resolution spectra are supplemented by higher resolution spec-
tra. For example, in the hydrocarbon work discussed below,
ions at both 91 and 92 amu are present. The total intensity
of this doublet is recorded with low resolution where the
peaks completely overlap and the contribution of each peak
is assigned by high resolution spectra. This works well since
mass discrimination is rarely important for ions separated by
one amu.
ꢀ
SF6 þ H2O $ SF6ꢀ(H2O)
(2)
SF6ꢀ(H2O) þ H2O - SF4Oꢀ þ 2HF þ H2O
(3a)
SF6ꢀ(H2O) þ H2O - Fꢀ(HF)2(H2O)0,1
þ [ SF3O(H2O)1,0 ],
(3b)
In the TIFT, the amount of clustering in the products is
controlled by secondary equilibrium and does not represent
the nascent distribution. For the alcohols the products are
Fꢀ(HF) and Fꢀ(HF)2 solvated to an indeterminable extent.
ꢀ
The slope of the decline in the SF6 signal vs. solvent
squared yielded the product of the equilibrium constant for
reaction (2) and the rate constant for reaction (3). The ratio of
[SF6ꢀ][X]]/[SF6ꢀ(X)] would be expected to yield the equili-
brium constant. The ratio was found not to depend on solvent
concentration of the solvent X as expected for equilibrium.
However, it was found that the ratio was dependent on
pressure, which was interpreted to involve clustering in the
supersonic expansion. Fortunately, equilibrium constants were
available from other measurements and rate constants could be
derived. The rate constants for reaction (3) were found to be
very small and pressure independent within a larger than
normal error (factor of two). For H2O, CH3OH, and
C2H5OH, the rates averaged to be 0.32, 1.9 and 2.2 ꢂ 10ꢀ13
cm3 sꢀ1, respectively. These values would be extremely difficult,
if not impossible, to measure in a low pressure or non flow
apparatus.
The branching ratios depend on pressure. Fig. 4 shows the
fraction of the Fꢀ(HF)2(ROH)n product vs. pressure. As a
reminder, the other product is SF4Oꢀ for H2O and
Fꢀ(HF)(ROH)n for the alcohols. The branching for the H2O
case is approximately constant. This indicates that the pro-
ducts may separate quickly on the time scale of collisions with
N2. For the alcohols, the Fꢀ(HF)2(ROH)n products increase
substantially with pressure at the expense of the
Fꢀ(HF)(ROH)n channel. A larger effect is observed for
C2H5OH. This was speculated to be a result of a two step
During sampling a supersonic expansion is formed. Cluster-
ing in the expansion can be a problem. It is difficult to
determine whether clustering occurred in the flow tube or in
the expansion. In one of our studies (see below) it was clear
that some of the clustering did occur in the expansion. In that
case, we could tell because the equilibrium constants were
known. For other species, this is difficult to determine espe-
cially when the temperature is not at 300 K because the area
near the nose cone may have a slightly reduced temperature,
which of course affects the equilibrium constant. For this
reason we have avoided pure clustering studies.
We have also worried about dissociation in the sampling
region. If the electric fields are high, dissociation can occur. We
check this by varying the electric field and looking for changes
in distributions. At the highest voltages we apply, dissociation
has been observed. We believe we have eliminated dissociation
for the most part by using reduced fields. The one exception is
in our original study of SF6ꢀ with SO2 where dissociation was
calibrated.
Results and discussion
The first study using the TIFT was of the reaction of SF6ꢀ with
SO2 at 300 K over the pressure range 25–700 Torr.8 This was
mainly a proof-of-principle study for which we did not expect
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5
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to be made.20 After numerous collisions, a Boltzmann distri-
bution of energies is found as indicated by the thermal dis-
tribution in the far right panel of Fig. 5. At high temperatures,
1
the distribution extends into the range where C8H10 can
dissociate and thermal dissociation takes place. As will be
shown below, both stabilization and dissociation have been
observed with both ethylbenzene and propylbenzene.
The first system studied was O21 with C8H10 (ethylbenzene)
over the temperature range from 423 to 573K.19,20 The lower
limit was set by the temperature where the water impurity led
1
to an unacceptable amount of non-O2 ions and the upper
limit was set partly by experimental constraints (see above) and
partly by the desire to avoid thermal dissociation in that study.
Current studies have led to an increase of the upper tempera-
ture limit so that the thermal dissociation process can be
studied. Mostly an N2 buffer was used but several points were
also taken in He. The mechanism depicted in Fig. 5 in the
absence of thermal dissociation can be summarized as
Fig. 4 Branching fraction of the Fꢀ(HF)2(ROH)n channel for the
reactions of SF6 with H2O, CH3OH and C2H5OH as a function of
ꢀ
pressure. (Parentheses indicate that the nature of the neutrals is
unknown.)
1
1
O2 þ C8H10 - C8H10 þ O2 (k ¼ akcap
)
1
O2 þ C8H10 - (C8H101)* þ O2 (k ¼ (1 ꢀ a)kcap
)
(C8H101)* þ M - C8H10 þ M (k ¼ gcZ)
1
mechanism where the second step is slow compared to buffer
gas collisions. The buffer gas can cool the complex allowing for
more time for the second proton transfer to occur. Alterna-
tively, the cooling can prevent HF from evaporating from a hot
intermediate. The latter explanation is more in line with our
charge transfer work discussed below.
(C8H101)* - C7H7 þ CH3 (k ¼ k(E))
(4)
1
where kcap is the capture rate constant, gc is the stabilization
efficiency, Z is the collision rate with respect to the buffer, and
1
k(E) is the dissociation rate as a function of energy. The C7H7
ion has two isomeric forms; benzylium, a six membered ring,
and tropylium, a seven membered ring. Most of the product is
the former, since it results from a simple benzylic bond
cleavage.25 There are minor products (see Fig. 3) which are
no more abundant than the impurity ions and were not
followed.
The most recent studies have involved charge transfer from
O21 to alkylbenzenes.18–20 In these experiments, the buffer gas
affects the reactivity in two ways. The processes occurring are
shown schematically for the ethylbenzene reaction in Fig. 5.
1
Reaction is started by charge transfer, which leaves the C8H10
ion in excited states which partially dissociate. The amount of
and rate for dissociation depends on the charge transfer
mechanism.21 A direct resonant mechanism leaves essentially
all alkylbenzene ions with enough energy to dissociate as
indicated by the distribution marked direct; the resonant
charge transfer product has an excitation energy of about
4 eV, much greater than thermal. If the reaction proceeds
through a complex, the distribution of alkylbenzene ions is
much broader and part of the distribution will not have enough
energy to dissociate. This is indicated by the fraction a in the
diagram. At low pressure, all molecules with energy above the
dissociation limit are expected to dissociate unless radiative
quenching or wall collisions compete with dissociation.
The dissociation of alkylbenzene ions takes place on the time
scale of collisions with the buffer gas.22–24 Thus, increasing the
pressure increases the amount of the nondissociative parent ion
observed by cooling the distribution. A collision with a buffer
gas molecule removes an average energy per collision hDEi.20
Combining TIFT measurements of the branching ratio for
stabilized parent to dissociated fragments (S/D) with measure-
ments of the unimolecular rate constants for dissociation as a
function of energy allows for a derivation of hDEi per collision
Rate constants were found to be equal to the collisional
value and independent of both temperature and pressure. This
was expected based on the low pressure results. In contrast, the
branching ratios were found to be highly pressure and tem-
1
perature dependent. Fig. 6 shows the ratio of C8H101 to C7H7
as a function of the N2 buffer gas density. The data clearly
show that the buffer gas is quenching the dissociation. Increas-
ing pressure increases the ratio linearly within the scatter in the
data. Increasing the temperature results in a shallower slope.
The intercepts show no measurable trend. Measurements made
using helium buffer at 523 K also yield linear data but with a
shallower slope than that found for N2 at the same tempera-
ture. This shows that N2 is a better quencher than He as
expected. Solving the kinetics in reaction (4) yields the
1
1
Fig. 6 Ratio of C8H10 to C7H7 yield as a function of N2 number
density for the reaction of O21 with C8H10. The lines are model fits to
the data as explained in the text. K, ’ and m refer to data at 423, 473
and 523 K, respectively.
1
Fig. 5 Schematic view of the processes started by the reaction of O2
with C8H10 (ethylbenzene).
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following expression for the branching ratio (S/D),
Â
uncertainty limits, equivalent to those of neutral toluene at
the same energy.29 Thus, the main difference between energy
transfer between ions and neutrals is due to the collision rate
and not the amount of energy transferred. Because the energy
transfer probably takes place on the repulsive part of the
potential, which is likely similar for both ions and neutrals,
the equivalence is not surprising. This contrasts to vibrational
energy transfer for low lying states.30 In that state-to-state
regime, energy transfer is dominated by complex formation for
ions and is much faster than that found for the corresponding
neutrals.
Ã
C8Hþ10
C7Hþ7
a
gcZ½Mꢄ
Â
[M] in accord with the data within our error.
Ã
ꢃ
þ
ð5Þ
1 ꢀ a
ð1 ꢀ aÞkðEÞ
This simple one-state model predicts a linear dependence on
gcZ
In this model, the slope of the TIFT data is ð1ꢀaÞkðEÞ. There-
fore, knowledge of k(E) allows gc to be derived. Additionally it
has been shown that if k(E) p (E ꢀ E0)s*ꢀ1 then hDEi can be
derived from
The above experiments and calculations were repeated using
n-propylbenzene as the reactant neutral.18 It was possible to
extend the conditions of the measurements in two ways. First,
the amount of water vapor impurity was reduced by fixing
leaks and baking the apparatus; this allowed minor products to
be measured accurately. Secondly, the upper temperature limit
was increased to allow for thermal decomposition studies. This
involved replacing seals and installing the star shaped heat
exchanger and clamshell heaters. The minor channels appeared
to behave similarly to the main dissociation channel forming
C7H71, i.e. quenching the charge transfer complex affected all
channels equally within our uncertainty.
gc
ꢀhDEisꢅ
ꢃ
ð6Þ
1 ꢀ gnc Eac ꢀ E0
where Eac is the energy of C8H101* after charge transfer, n is an
exponent close to 2, and E0 is the bond dissociation energy.26
k(E) has been measured by two groups but outside our
energy range.23,24 To compensate, statistical adiabatic channel
model/classical trajectory (SACM/CT) calculations have been
made.27 The details of the calculations are only summarized
here. A model potential is used such that in the reaction
coordinate it is a mix of (a) a long-range, charge-induced
dipole potential and (b) a short-range valence potential. An-
isotropy is also included in the short-range valence potential.
Conserved modes are treated by SACM and the bond breaking
modes are treated by CT. The absolute magnitude of k(E) is
fixed at a single point by adjusting the bond dissociation
energy. It is shown that pure statistical calculations are not
valid because the Massey parameter indicates that the dy-
namics are non-adiabatic. The k(E) curves fit the complete
There was enough scatter to prevent detection of small
changes.
Adding a thermal dissociation channel,
1
1
C9H12 þ M - C7H7 þ C2H5 þ M,
(7)
creates kinetics that are slightly more complicated. If one
assumes that either the excited state charge transfer product
experimental data set and are proportional to (E ꢀ E0)s*ꢀ1
Thus, eqn. (6) can be used to calculate hDEi.
.
1
dissociates or a Boltzmann distribution of C9H12 dissociates
one derives,
While the above discussion gives the underlying theory for
such derivations, it is of course better to account for broad
energy distributions arising from charge transfer. This has also
been done. The first step is to derive the energy distributions in
C8H101* after the charge transfer but before quenching. Three
mechanisms are possible, (a) resonant charge transfer, (b)
complex formation followed by a statistical dissociation into
the products, and (c) production of electronically excited O2.
The first two are depicted in Fig. 5 and the latter contributes
only to a. Statistical theory is used to calculate the energy
distributions for each mechanism. In order to assign contribu-
tions to each of the mechanisms, three data sets were com-
S
ðS=DÞ ½ 1 ꢀ expðꢀktdtÞ ꢄ
ktdt 1 þ ðS=DÞ00 ꢀ ðS=DÞ ½ 1 ꢀ expðꢀktdt Þꢄ
À
Á
ꢃ
ð8Þ
D
0
where S/D, the stabilization-to-dissociation ratio, is the ratio
1
of C9H12 to C7H71, (S/D)0 is this ratio in the absence of
thermal dissociation, and ktd is the thermal dissociation rate
constant. This expression refers to the zero depletion limit,
which is a good assumption since the branching ratio data are
obtained by extrapolating to zero concentration of C9H12.
(S/D)0 and ktd are obtained separately by studying the kinetics
at various reaction times by moving the inlet. Data obtained at
100 Torr and at two temperatures are shown in Fig. 7. The
lines are non-linear least squares fits using eqn. (8). The
thermal dissociation study was performed at 573 and 603 K
as a function of pressure. Table 1 shows the thermal
1
bined. The fraction of non-dissociated C8H10 in ICR25 and
molecular beam experiments28 at near zero pressure is assigned
as the fraction corresponding to mechanism (c) since the
production of excited state O2 leads exclusively to products
that do not dissociate. The TIFT extrapolation to zero pressure
does not equal the low pressure values and one Torr measure-
ments are in between the extrapolated TIFT and the low
pressure value. These facts indicate that both of the other
mechanisms are operative and allow for assignment of the
probability of mechanisms (a) and (b). In this way, the assigned
probabilities are 0.26, 0.56 and 0.18 for mechanisms (a)–(c),
respectively. The data did not warrant a temperature depen-
dence of these fractions but the distributions were allowed to
be temperature dependent. The ratio of C8H101 to C7H71 was
calculated and shown in Fig. 6 for each temperature. The
calculations fit the data very well and show that the data
would curve at pressures lower than can be measured in the
TIFT. The intermediate pressure range is due to the changing
distribution of the complex-forming channel. The pressure
range in low pressure flow tubes is not large enough to measure
an appreciable dependence accurately.
Finally, it is possible to derive hDEi, the average energy
transferred per collision. Using the best estimates of the
various contributions to the mechanism above, hDEi is found
to be 285 ꢁ 150 cmꢀ1 for N2 and 180 ꢁ 90 cmꢀ1 for He at an
average energy of 26 600 cmꢀ1. These values are, within
Fig. 7 The ratio of [C9H121]/[C7H71] is plotted vs. reaction time at
pressures of 100 Torr of N2 for the reaction of O21 with C9H12. Fits to
eqn. (8) are shown as curves.
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5
P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 1 5 3 3 – 1 5 3 9
1537

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1
Table 1 Thermal dissociate rate constants of C9H12 from O2
1
þ
C9H12 as a function of temperature and pressure
T/K
P/Torr
ktd/sꢀ1
573
50
75
37
44
100
150
200
250
30
32
22
27
34
101
603
50
75
109
109
98
100
150
200
250
75
109
138
1
Fig. 9 Recombination rate constants kcap ¼ krec,00 for C2H5 þ C7H7
1
.
The lines are from modeling, see text. The single point is from
measurements of the thermal decomposition of C9H12 after conver-
sion through the equilibrium constant.
dissociation rates. The data are somewhat scattered with the
603 K data being less so due to the larger rate constant which
suggests that the measurements at 603 K are more reliable.
Because the data are independent of pressure with experi-
mental error, this indicates that the system is in the high
pressure regime. As explained below, calculations confirm this
conclusion.
certainly contribute. Nonetheless, the derived hDEi value is not
1
particularly sensitive and was found to be 200 ꢁ 100 cmꢀ1
,
which, within error, is the same as for C8H10 and again
similar to the value for neutral propylbenzene.31
In order to test the fit, calculations of the thermal dissocia-
tion rate were performed using the same expression for k(E)
including the J dependence. Without adjusting any parameters,
relatively good agreement between the measured, pressure-
averaged value at 603 K, i.e., ktd ¼ 106 sꢀ1 and the predicted
value of 46.9 sꢀ1 was found, see Fig. 9. This implies that
everything is self-consistent and fixes the bond dissociation
Fig. 8 shows the S/D data and model fits. Included is (S/D)0
1
when thermal dissociation plays a role in the kinetics. C8H10
and C9H121 have nearly equal dissociation energies. Because of
the larger number of oscillators, one would expect that k(E), at
1
1
the same E ꢀ E0, is smaller for C9H12 than for C8H10
.
However, because the two molecules apparently have different
energy to be E0 ¼ 166.9 ꢁ 4.2 kJ molꢀ1
.
distributions of oscillator frequencies, k(E) is about a factor of
1
two larger for C9H12 than the corresponding value for
It is important to point out that the high pressure limiting
rate constant for the reverse recombination reaction of C2H5
with C7H71, krec,N(T), such as given by,
C8H101. As a consequence, higher pressures for collisional
1
stabilization are required for C9H12 than for C8H10
1
.
A derivation that is as detailed as for the ethylbenzene
reaction proved difficult for two reasons. Firstly, it was not
possible to precisely assign fractions to the various mechan-
isms. Secondly, the k(E) data are not known as well. In any
case, a similar analysis was done and the results are shown in
Fig. 8. It is clear that the results do not fit the data as well for
reasons that are not obvious although the reasons cited above
k
rec,N(T) E 8.0 ꢂ 10ꢀ12 (T/600 K)ꢀ1.16 cm3 moleculeꢀ1 sꢀ1
is much smaller than the Langevin rate constant, kL ¼ 1.0 ꢂ
10ꢀ9 cm3 moleculeꢀ1 sꢀ1. In other words, krec,N(T) is expected
to be much smaller than the Langevin rate constant in the
1
capture of C2H5 by C7H7
.
Finally, we have extended the temperature range of the
instrument even higher (673 K) to study the thermal dissocia-
tion of C8H101, which occurs at somewhat higher temperatures
than does C9H121. The results were found to be consistent
with the thermal decomposition of C9H121, i.e. the data
indicate that the high pressure limit was observed.32 A statis-
tical calculation of the complete fall-off curves for both
ethylbenzene and propylbenzene cations was also performed32
so that the data can be used in plasma-enhanced combustion
models. A statistical calculation of the complete fall-off curves
for both ethylbenzene and propylbenzene cations will be
performed so that the data can be used in plasma-enhanced
combustion models.
Conclusions
While relatively few studies have been made with the TIFT at
AFRL, its value as a new instrument has been proven. The first
study of SF6ꢀ with SO2 provided no new data but showed that
the instrument is capable of accurate measurements over a
wide pressurꢀe range. This was exploited in studying the reac-
tions of SF6 with various solvents where it was found that
reaction proceeds in two steps and that the rates are very slow.
It is doubtful that as much information could be obtained in
any other type of apparatus that is currently available. The
large pressure and temperature ranges accessible allowed
unique data to be obtained in the charge transfer studies of
1
1
Fig. 8 Ratio of C9H12 to C7H7 yields as a function of N2 number
density for the reaction of O21 with C9H12. The lines are model fits to
the data as explained in the text. Squares, triangles, diamonds, and
crosses refer to data at 448, 473, 523 and 573 K, respectively.
1538
P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 1 5 3 3 – 1 5 3 9
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

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1
O2 with alkylbenzenes. Parent alkylbenzene ions were found
10 A. A. Viggiano and S. Williams, in Advances in Gas Phase Ion
Chemistry, ed. N. G. Adams and L. M. Babcock, Academic Press,
New York, 2001, pp. 85–136.
11 A. A. Viggiano and R. A. Morris, J. Phys. Chem., 1996, 100,
19227–19240.
12 R. L. Daugherty and J. B. Franzini, Fluid Mechanics with En-
gineering Applications, McGraw-Hill, New York, 7th edn., 1977.
13 M. Gilbert, Combust. Flame, 1958, 2, 149–156.
14 F. C. Fehsenfeld, M. Mosesman and E. E. Ferguson, J. Chem.
Phys., 1971, 55, 2115–2120.
to be stabilized at high pressure and to pyrolyze at high
temperatures. Combining the data with k(E) measurements
and rate theory allowed energy transfer parameters to be
measured. It was also found that the magnitude of energy
transfer of ions is comparable to that of the neutral counter-
parts. The analysis also allows bond energies to be derived
accurately.
15 Y. Ikezoe, S. Matsuoka, M. Takebe and A. A. Viggiano, Gas
Phase Ion-Molecule Reaction Rate Constants Through 1986,
Maruzen Company Ltd, Tokyo, 1987.
Acknowledgements
16 L. G. Huey, D. R. Hanson and C. J. Howard, J. Phys. Chem.,
1995, 99, 5001–5008.
17 S. T. Arnold and A. A. Viggiano, J. Phys. Chem. A, 2001, 105,
3527–3531.
18 A. I. Fernandez, A. A. Viggiano, T. M. Miller, S. Williams,
I. Dotan, J. V. Seeley and J. Troe, J. Phys. Chem. A, 2004, 108,
9652–9659.
19 A. A. Viggiano, T. M. Miller, S. Williams, S. T. Arnold,
J. V. Seeley and J. F. Friedman, J. Phys. Chem. A, 2002, 106,
11917–11922.
This project was funded by the United States Air Force Office
of Scientific Research under Project 2303EP4 and Grant
Award FA8655-03-1-3034. Financial support of our work by
the European Office for Aerospace Research (EOARD grant
FA8655-03-1-3034) and by the Deutsche Forschungsge-
meinschaft (SFB 357 ‘Molekulare Mechanismen unimoleku-
larer Prozesse’) is gratefully acknowledged.
20 J. Troe, A. A. Viggiano and S. Williams, J. Phys. Chem. A, 2004,
108, 1574–1581.
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T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5
P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 1 5 3 3 – 1 5 3 9
1539