Shock tube study of dissociation and relaxation in 1,1-difluoroethane and vinyl fluoride

Article abstract of DOI:10.1039/b703124f

This paper reports measurements of the thermal dissociation of 1,1-difluoroethane in the shock tube. The experiments employ laser-schlieren measurements of rate for the dominant HF elimination using 10% 1,1-difluoroethane in Kr over 1500-2000 K and 43 < P < 424 torr. The vinyl fluoride product of this process then dissociates affecting the late observations. We thus include a laser schlieren study (1717-2332 K, 75 < P < 482 torr in 10 and 4% vinyl fluoride in Kr) of this dissociation. This latter work also includes a set of experiments using shock-tube time-of-flight mass spectrometry (4% vinyl fluoride in neon, 1500-1980 K, 500 < P < 1300 torr). These time-of-flight experiments confirm the theoretical expectation that the only reaction in vinyl fluoride is HF elimination. The dissociation experiments are augmented by laser schlieren measurements of vibrational relaxation (1-20% C₂H₃F in Kr, 415-1975 K, 5 < P < 50 torr, and 2 and 5% C₂H₄F₂ in Kr, 700-1350 K, 6 < P < 22 torr). These experiments exhibit very rapid relaxation, and incubation delays should be negligible in dissociation. An RRKM model of dissociation in 1,1-difluoroethane based on a G3B3 calculation of barrier and other properties fits the experiments but requires a very large 〈ΔE〉_down of 1600 cm^-1, similar to that found in a previous examination of 1,1,1-trifluoroethane. Dissociation of vinyl fluoride is complicated by the presence of two parallel HF eliminations, both three-center and four-center. Structure calculations find nearly equal barriers for these, and TST calculations show almost identical k_∞. An RRKM fit to the observed falloff again requires an unusually large 〈ΔE〉_down and the experiments actually support a slightly reduced barrier. These large energy-transfer parameters now seem routine in these large fluorinated species. It is perhaps a surprising result for which there is as yet no explanation. the Owner Societies.

Full text of DOI:10.1039/b703124f

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PAPER
www.rsc.org/pccp | Physical Chemistry Chemical Physics
Shock tube study of dissociation and relaxation in 1,1-difluoroethane and
vinyl fluoride
Hui Xu,a John H. Kiefer,*a Raghu Sivaramakrishnan,b Binod R. Giric and
Robert S. Tranter*c
Received 1st March 2007, Accepted 16th April 2007
First published as an Advance Article on the web 24th May 2007
DOI: 10.1039/b703124f
This paper reports measurements of the thermal dissociation of 1,1-difluoroethane in the shock
tube. The experiments employ laser-schlieren measurements of rate for the dominant HF
elimination using 10% 1,1-difluoroethane in Kr over 1500–2000 K and 43 o P o 424 torr. The
vinyl fluoride product of this process then dissociates affecting the late observations. We thus
include a laser schlieren study (1717–2332 K, 75 o P o 482 torr in 10 and 4% vinyl fluoride in
Kr) of this dissociation. This latter work also includes a set of experiments using shock-tube time-
of-flight mass spectrometry (4% vinyl fluoride in neon, 1500–1980 K, 500 o P o 1300 torr).
These time-of-flight experiments confirm the theoretical expectation that the only reaction in vinyl
fluoride is HF elimination. The dissociation experiments are augmented by laser schlieren
measurements of vibrational relaxation (1–20% C2H3F in Kr, 415–1975 K, 5 o P o 50 torr, and
2 and 5% C2H4F2 in Kr, 700–1350 K, 6 o P o 22 torr). These experiments exhibit very rapid
relaxation, and incubation delays should be negligible in dissociation. An RRKM model of
dissociation in 1,1-difluoroethane based on a G3B3 calculation of barrier and other properties fits
the experiments but requires a very large hDEidown of 1600 cmꢀ1, similar to that found in a
previous examination of 1,1,1-trifluoroethane. Dissociation of vinyl fluoride is complicated by the
presence of two parallel HF eliminations, both three-center and four-center. Structure calculations
find nearly equal barriers for these, and TST calculations show almost identical kN. An RRKM
fit to the observed falloff again requires an unusually large hDEidown and the experiments actually
support a slightly reduced barrier. These large energy-transfer parameters now seem routine in
these large fluorinated species. It is perhaps a surprising result for which there is as yet no
explanation.
question the interpretation5,6 of the original ST/LS results. In
Introduction
any case, it seems that further study of this and related
The decomposition of the fluorinated ethanes is often domi-
reactions is strongly indicated. One possible experimental
nated by simple molecular HF elimination. As such this
approach to further understanding might be through an
reaction, with just one channel and often stable products, is
investigation of HF elimination from other partially fluori-
ideal for investigation by non-specific methods, i.e., those that
nated ethanes. All of these are readily available from various
do not provide an actual product analysis, such as the shock
sources.
We have argued before1 that the ST/LS method is uniquely
tube/laser-schlieren (ST/LS) technique in incident shock
waves. Previously we used this to explore such HF elimination
suited to the examination of possible non-statistical effects in
in 1,1,1-trifluoroethane1 at very high temperatures (1600–
thermal dissociation, because for relatively slow IVR rates to
2400 K), and found an anomalous falloff suggesting a possible
noticeably retard such reaction, the reaction still needs to
non-RRKM process. A ‘failure’ of statistical theory in a
proceed, at least, in part, at something like a comparable
speed. Given the evident speed of IVR processes,7 it seems
simple thermal reaction such as the HF elimination that occurs
some involved k(E) will certainly need to exceed 108 sꢀ1. This
in 1,1,1-trifluoroethane is certainly surprising and unprece-
will minimally require overall rates in excess of 106 sꢀ1
,
dented, although the possibility of such an occurrence, per-
haps through slow IVR, has been well-recognized and
extensively discussed since the theory’s inception.2–4 In fact,
this result has now led to theoretical studies that seriously
necessitating high temperatures—and also large molecules,
so the reaction is not simply at the low-pressure limit where
intermolecular energy transfer is controlling. The ST/LS tech-
nique is one of the few methods capable of accurate thermal
rate determination for such circumstances.
a Department of Chemical Engineering, University of Illinois at
Chicago, Chicago, IL 60607, USA
The ST/LS method measures density gradient by narrow
laser-beam deflection in the incident-shock flow, and this
provides both high resolution and sensitivity to fast processes.
Unfortunately, it also entails some serious limitations in its
b Department of Mechanical and Industrial Engineering, University of
Illinois at Chicago, Chicago, IL 60607, USA
c Chemistry Division, Argonne National Laboratory, Argonne, IL
60439, USA
ꢁc
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4164 | Phys. Chem. Chem. Phys., 2007, 9, 4164–4176

application which are discussed here. The relation between
gradient and rate for a single reaction occurring in an ideal
ture calculation forms an essential part of the treatment of
both dissociation reactions.
incident shock is8
Treatment of the vinyl fluoride dissociation introduces a
further complication through the occurrence of two paths for
the process, a three-center elimination to vinylidene which
quickly reverts to acetylene, reaction (2) and a four-center
elimination giving acetylene directly, reaction (3).18,19
ꢀ
P
dr
r
rðDH ꢀ CpTDNÞ
¼
dx r0uðCpT=M ꢀ Cnn2=RÞ
Thus the gradient is proportional to the rate, r, through the
heat of reaction DH, with a (usually) small reduction from
expansion through any increase in mole number DN. The
remaining quantities are just molecular heat capacities or
incident shock parameters, easily obtained from measure-
ments or calculations.8 Accordingly, application will run into
difficulty when the difference DH ꢀ CpTDN is too small, as in a
close to thermoneutral reaction.
C2H3F ! CH2C : þ HF
ð2Þ
CH2C : ! C2H2
C2H3F ! C2H2 þ HF
ð3Þ
This complication does, however, add a further reason for
undertaking a study of the thermal dissociation of vinyl
fluoride. The branching between the two routes for this has
been discussed both theoretically18–20 and experimentally20
using molecular-beam laser photolysis, and it seems that both
must be heavily involved, but no evaluation of the thermal
ratio has appeared.
We now consider the group of all hydrofluoroethanes in
light of the above equation and the prior literature.
(1) Monofluoroethane. Here reaction is certainly dominated
by HF elimination,9–12 but the heat of reaction, DH0298, is a
mere 10.4 kcal molꢀ1, and this is nearly cancelled by the usual
10–15 kcal molꢀ1 from CpTDN, with DN = +1. Thus ST/LS
experiments would be effectively blind to this reaction.
(2) 1,1-Difluoroethane. Again dominated by HF elimination
with DH0298 = 23.19 kcal molꢀ1— still small, but acceptable.
Reaction (1) in this paper.
Experimental
A. ST/LS
(3) 1,2-Difluoroethane. HF elimination has DH2098= 10.03
kcal molꢀ1, again too small.
The shock tube used in the LS experiments has a 4 ft long
driver section of 4 in. id connected to a 10 ft driven section of
2.5 in. id, whose detailed layout has been very fully de-
scribed.21 The ST/LS diagnostics have also been described
previously.8 The data acquisition system for the LS experiment
has been upgraded, giving improved sensitivity and resolution,
but again this has been fully described elsewhere.22,23 In
addition to the improved hardware, the control and analysis
software have also been updated. This software determines
chemically frozen, but vibrationally equilibrated, ideal-shock
parameters and also calculates the Blythe and Blackman
corrections22–24 used in the analysis of vibrational relaxation
time. As before,21 velocities were set by interpolation of four
intervals calculated from measured times centered about the
LS beam. On the basis of extensive experience, the uncertainty
in velocity is estimated as ꢂ0.2%, corresponding to a tem-
perature error of less than ꢂ0.5%, here amounting to the
order of ꢂ10 K.
(4) CHF2CH2F. DH2098 = 35.1 kcal molꢀ1. Here there is
more than enough heat of reaction, but the path to HF is
ambiguous: this is not the necessary simple, unambiguous
process.
(5) CH3CF3. DH0298 = 35.1 kcal molꢀ1, and the subject of
our earlier work.1
(6) Of the remainder, CF3CH2F, and both CHF2CHF2 and
CHF2CF3, involve considerable CC bond fission.13–16
Thus, only the subject of this paper, 1,1-difluoroethane,
seems to meet all the criteria for the study of HF elimination
by LS.
1,1-Difluoroethane evidently dissociates solely by loss of
HF17 to produce vinyl fluoride and this may subsequently
dissociate to acetylene and HF.
C2H4F2 ! C2H3F þ HF
ð1Þ
Unfortunately, the dissociation of vinyl fluoride is facile
enough to produce small but discernible gradient at later times
and high temperatures, and so must be taken into account in
the modeling. This paper thus includes a separate examination
of both relaxation and dissociation of vinyl fluoride, and the
results of this are used in the modeling of the difluoroethane
dissociation. Here this last reaction is examined using both ST/
LS and shock tube/time-of-flight mass-spectrometric (ST/
TOF-MS) measurement of reactants and products in a sepa-
rate apparatus. The ST/TOF-MS results complement the ST/
LS experiments by providing both additional kinetic data and
time-resolved species profiles that, here, serve to confirm the
absence of any bond-fission reactions or formation of second-
ary products. Furthermore, there is good overlap between the
experimental ranges of the ST/LS and ST/TOF-MS experi-
ments with the latter generally permitting extension to lower
temperature and higher pressure. A separate electronic struc-
To produce the very weak shocks necessary for observation
of the fast relaxation in these fluorides, a slow flow of driver
gas was achieved by introducing various converging/diverging
nozzles of different throat diameters at the diaphragm. The
experiments all used Mylar diaphragms of 0.001–0.005 inch
thickness, burst spontaneously with helium. Molar refractiv-
ities used in the calculation for density gradient from measured
angular deflection were 10.99 for 1,1-difluoroethane,25 10.725
for vinyl fluoride25 and 6.367 for Kr.26 These were taken as
constant throughout the decomposition; an excellent approx-
imation for such species.
In addition to the ST/LS experiments performed with the
above apparatus a number of ST/LS experiments were per-
formed on vinyl fluoride dissociation using the ST/TOF-MS
apparatus (see below) which is also equipped for laser schlie-
ren studies behind the incident shock wave.27,28 The internal
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Fig. 1 Schematic of the ST/TOF-MS interface. The inset shows the end of the shock tube and the nozzle/skimmer arrangement in detail. PT1 to
PT4 are the sidewall pressure transducers. For clarity the end wall pressure transducer PT5 is not shown. The electron gun, not shown, is located
on the top of the ion source chamber pointing into the page.
diameters of both shock tubes are identical in the LS sections
and both use identical detectors and similar lasers. These
experiments again serve to confirm the performance of the
new LS setup.
nozzle/skimmer arrangements before selecting the arrange-
ment used herein. A schematic of the nozzle/skimmer interface
is shown in Fig. 1.
Ions are generated from the molecular beam by electron
impact ionization with an electron energy of 30 eV which
minimizes ionization of the bath gas, neon. Packets of ions are
injected into the drift section of the TOF-MS, via ion optics, at
9.52 ms intervals (105 kHz) where they are separated by mass/
charge, m/z, and subsequently detected with a Chevron stack
multichannel plate detector, MCP. During an experiment the
output of the MCP is acquired for 1–2 ms and the data
represent mass spectra from before the arrival of the shock
wave at the driven section end wall and after generation of the
reflected shock wave. Simultaneously, the timing signals used
to generate and inject the ion packets are captured and using
in-house software the output of the MCP is split into discrete
mass spectra for each ionization event. An example of the
MCP output and the associated timing signals is given in
Fig. 2a, and a discrete spectrum extracted from Fig. 2a is
shown in Fig. 2b where the ions are identified. Ions are
identified by their flight time (tf), the time that elapses from
injection into the TOF-MS to arrival at the MCP, and this is
converted to m/z by
Reagent mixtures
1,1-Difluoroethane and vinyl fluoride were obtained from
SynQuest Laboratories, Inc. (99% min. purity), and krypton
was Spectra Gases excimer grade. Mixtures were prepared
manometrically in a 50-L glass vessel and stirred for 2 h using
a Teflon-coated magnetic stirrer. Mixtures of 2, 5, and 10% of
C2H4F2 in Kr and 1, 4, 5, 10 and 20% C2H3F in Kr were used,
with uncertainties in composition of less than ꢂ0.1%.
B. ST/TOF-MS
This is a recently developed apparatus that has been described
in detail elsewhere,27,28 and only a brief overview is given here.
In contrast to the ST/LS technique where measurements are
made behind the incident shock wave, the ST/TOF-MS meth-
od studies reactions behind the reflected shock wave by
continuously drawing samples through an open orifice cen-
tered in the endwall of the driven section of the shock tube.
The orifice forms the first stage of a nozzle/skimmer sampling
system that rapidly quenches the sampled gases and forms
them into a molecular beam that flows into the ion source of a
reflectron TOF-MS. The sampling apparatus has been con-
structed to ensure that the molecular beam is not contami-
nated by gases from the cold thermal boundary layer that
grows from the end wall behind the reflected shock wave.28 As
reported in ref. 27 and 28, we have investigated numerous
m
2
¼ aðtf Þ þ b
z
Here, a and b are constants determined by measuring the flight
times of known species for a particular operational setting of
the TOF-MS.
Shock waves are initiated in the ST/TOF-MS by puncturing
aluminum diaphragms with a four-bladed, sharp-tipped knife
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Reagent mixtures
The reagents, vinyl fluoride (Synquest Laboratories Inc., 99%
min. purity), krypton (Spectra Gases, excimer grade), argon
(Linde, 99.999%) and neon (Linde, 99.999%), were used as
supplied. Mixtures containing 2 or 4% of vinyl fluoride and
4% argon, as internal standard, in neon, were prepared for the
TOF-MS experiments. The reaction mixtures were prepared in
a 50 L glass vessel that had been evacuated to o10ꢀ5 torr.
Mixtures were allowed to homogenize for at least 24 h before
use.
Unless otherwise noted, thermodynamic functions for
C2H4F2 and C2H3F (DfH0298, Cp and H1(T)ꢀDH0298) and for
other species encountered herein, were obtained from the
NIST compilations of S. E. Stein,29 the NIST computational
chemistry database30 and/or Burcat and Ruscic’s online data-
base of thermochemical properties.31
Vibrational relaxation
A. Vinyl fluoride
Relaxation in vinyl fluoride was observed over 415–1975 K in
mixtures of 1, 5, and 20% C2H3F in Kr, for pressures between
5 and 50 torr. Examples of ST/LS semi-log gradient profiles
showing a single-stage relaxation are presented in Fig. 3, and
relaxation times derived from plots like these are summarized
in Fig. 4. Here the separation between times for the differing
mixtures has been used for an extrapolation to a fit for pure
C2H3F and for C2H3F infinitely dilute in Kr, as shown. Also in
Fig. 4 is shown the one room temperature ultrasonic result for
the pure gas,32 seen to be in excellent agreement with a short
extrapolation of the derived fit to the pure gas. Fig. 5
illustrates the results of calculating hDEidown from these
relaxation times.33
Fig. 2 Results from a ST/TOF-MS experiment. Ion packets were
generated at 105 kHz (9.52 ms), T5 = 1764 K, P5 = 565 torr. The
repetition rate causes overlap of the spectra from successive time
periods (see ref. 28 for details of deconvoluting the data). The upward
pointing lines represent the timing signals. The downward pointing
lines represent the mass spectra. (a) Raw ST/TOF-MS data showing
both pre-shock and post-shock data. (b) One time segment from figure
(a). The flight times are relative to the falling edge of the leftmost
timing signal and the peaks at short flight times are from a previous
ionization event. Numbers in parentheses represent m/z and are
obtained by calibration.
As a test, the observed gradients have been integrated from
t = 0 to N assuming exponential behavior throughout, giving
a net density change34,35 of
1 ꢁ
ꢂ
ꢁ
ꢂ
Z
dr
dx
dr
dx
Drtotal
¼
u1eꢀt=tdt ¼
u1tini
0
t¼0
t¼0
and these are then compared with ‘thermodynamic’ Dr deter-
mined from the change in state from no relaxation to full
relaxation in the ideal shock. The result is an experimental
change generally near a factor of 2 too high, as shown in
Fig. 6. This kind of error is becoming routine for very fast
relaxation. It probably indicates a 0.1–0.2 ms error in t = 0, or
a non-exponential process in the earliest unobserved stages.
Again such deviations are routine for such fast relaxation and
are not regarded as a serious limitation on the validity of
relaxation times.
mounted on a shaft inside the driven section. This method
minimizes the creation of diaphragm fragments that may
block the sampling orifice in the driven section of the shock
tube and provides control of the reaction conditions by
permitting precise setting of initial conditions. A set of min-
iature piezoelectric pressure transducers (PCB 132A35), iden-
tified as PT1 to PT4 in Fig. 1, are mounted on the side wall of
the driven section and are used to obtain the incident shock
wave velocity close to the sampling orifice. The temperature
and pressure behind the reflected shock wave are obtained in a
similar manner to the incident shock conditions in the ST/LS
experiments with similar estimated errors in the post shock
temperature. PT1 is also used to generate a trigger signal for
the data acquisition system and initiate generation of ion
packets in the TOF-MS.27,28
In conclusion, it is seen that vinyl fluoride relaxes rapidly
but not quite with the extreme efficiency of the fluorinated
ethanes,1 where hDEidown can exceed 200 cmꢀ1. The rates of
relaxation found here are nonetheless sufficiently large that the
possibility of measurable incubation delays in the dissociation
may be safely discounted.
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Fig. 3 Density gradients generated by vibrational relaxation of vinyl fluoride, VF, in very low pressure experiments. The insets show semilog plots
of the displayed raw voltage measurements with solid-line fits. Here the temperatures/pressures are much too low for discernible dissociation and
these exponential gradients following the large diffraction refraction ‘spike’ are entirely from relaxation.
B. 1,1-Difluoroethane
Relaxation in 1,1-difluoroethane has been observed over
700–1350 K in mixtures of 2 and 5% C2H4F2 in Kr, and for
pressures between 6 and 22 torr. Examples of ST/LS semi-log
gradient profiles showing relaxation are presented in Fig. 7,
and relaxation times derived from plots like these are sum-
Fig. 4 Landau–Teller plot of derived vibrational relaxation times for
1% C2H3F/Kr: [’], 17–44 torr; 5% C2H3F/Kr: [K], 16–50 torr; 20%
C2H3F /Kr: [m], 5–30 torr. The results for the different concentration
were extrapolated to relaxation times for pure vinyl fluoride [—] and
vinyl fluoride infinitely dilute in Kr [. . .], as shown. The one room-
temperature relaxation time for pure vinyl fluoride [.] is from Fogg
and Lambert.32
Fig. 5 Derived hDEidown values for 1% C2H3F/Kr: [’], 17–44 torr;
5% C2H3F /Kr: [K],16–50 torr; 20% C2H3F /Kr: [m], 5–30 torr
(see text).
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Fig. 6 Density change ratio, Drexp/Drthermo, of relaxation experiment
to thermodynamic calculation: 1% C2H3F/Kr: [’], 17–44 torr; 5%
C2H3F /Kr: [K], 16–50 torr; 20% C2H3F/Kr: [m], 5–30 torr.
Fig. 8 Landau–Teller plot of vibrational relaxation times for 2%
C2H4F2/Kr: [’]; 9–22 torr; 5% C2H4F2/Kr: [K], 6–22 torr.
marized in Fig. 8. Note the negative temperature dependence,
a characteristic behavior for very fast relaxation in large
molecules. Also recognize that relaxation is so rapid here that
resolution is marginal, and these relaxation times should be
regarded as merely a rough estimate. In fact, they are so rapid
there is no possibility of detecting double relaxation.
calculations assume that Landau–Teller selection rules are
dominant, i.e., only single-quantum jumps are significant.
However, the calculations have also been done allowing all
transitions, with negligible change. Evidently here the lowest
molecular frequencies are large enough to block multiple
jumps.
Fig. 9 illustrates the results of estimating hDEidown from
these relaxation times.33 For both molecules these hDEidown
Fig. 7 Density gradients from vibrational relaxation of 1,1-difluoroethane, DFE, in very low pressure experiments whose temperatures/pressures
are much too low for discernible dissociation (see caption to Fig. 3).
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fluoride, near a factor of 2 too high. As before, such deviations
are routine for such fast relaxation and should not be a serious
limitation on the validity of relaxation times.
In conclusion, it is seen that 1,1-difluoroethane relaxes very
quickly, with a hDEidown routinely above 110 cmꢀ1, so that
excitation requires only a few collisions. Clearly the rates of
relaxation found here are also sufficiently large that the
possibility of measurable incubation delays may be dis-
counted.
Dissociation
A. Vinyl fluoride
Comparing reactions (2) and (3), both with barriers less than
75 kcal molꢀ1 (see below), other possible channels will cer-
tainly not be significant.36 Some such possible channels are:
(a) H-atom fission: CHFQCH2 - H + HCQCHF, with
Fig. 9 Derived hDEidown values for the single quantum jump assump-
tion (see text) in 2% C2H4F2/Kr [&] and 5% C2H4F2/Kr [J]. For
multiple jumps, the change is less than the scatter (see text).
DH0298 = 112 kcal molꢀ1
;
(b) CF fission: CHFQCH2 - F + H2CQCH, DH2098
124 kcal molꢀ1
(c) CC fission: CHFQCH2 - :CHF +:CH2, DH2098
174 kcal molꢀ1
=
=
As above, the observed gradients have again been integrated
assuming exponential behavior, giving an experimental esti-
mate of overall Dr.34,35 Again comparing with the thermo-
dynamic density change, the result is similar to that in vinyl
;
;
Fig. 10 Raw signals and semi-log density gradients [J] from examples of dissociation in 10 and 4% vinyl fluoride, VF, and modeling of these
(solid lines) for moderate to high pressures (see text). Here temperatures and pressures are all vibrationally relaxed, chemically frozen, ideal post-
incident shock values, and are used as the initial values in the modeling. The initial steep drop in each is again a consequence of shock-front
diffraction/refraction, and is ignored in the modeling. The late distortions evident beyond 2–3 ms following the schlieren spike for the higher
pressures are believed to arise from boundary layer turbulence, and are also ignored in the modeling. Here the first few ms’s of gradient are more
than adequate to set an accurate rate of dissociation.
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Fig. 12 Concentration/time profile from a ST/TOF-MS experiment,
T5 = 1870 K, P5 = 603 torr. [m] vinyl fluoride and [K] acetylene. The
solid lines represent the simulation.
Fig. 11 A TOF mass spectrum of pure vinyl fluoride taken in the ST/
TOF-MS, 30 eV ionization energy. The downward pointing peaks are
the mass spectrum. Flight times are measured relative to the injection
pulse shown by the vertical line at the left of the inset figure. Individual
peaks are identified and the m/z, in parentheses, obtained by cali-
bration.
Fig. 2b, a concentration/time profile for each experiment can
be developed that accurately represents the rapidly changing
conditions in the shock tube, Fig. 12. HF+ ions have almost
the same m/z as Ne+ ions, formed from the bath gas, and are
indistinguishable from them with the current instrument.
(d) H2 elimination: CHFQCH2 - H2 + HCCF, DH2098
64 kcal molꢀ1, a low value, but for this the barrier is actually
much higher; a G3B3 estimate is 108 kcal molꢀ1
=
+
.
Consequently, only C2H3F+ and C2H2 are considered in
Fig. 10 presents ST/LS density gradients showing dissocia-
tion in vinyl fluoride. These experiments cover 1717–2332 K,
75 o P o 482 torr in 10 and 4% vinyl fluoride in Kr. These
are generally at both higher pressures and higher temperatures
than the above examples of relaxation, and the relaxation
process is now lost in the shock-front signal, the ‘schlieren
spike’. Again, since vinyl fluoride relaxes rapidly, incubation
delays are negligible for these high pressure experiments.
Modeling of these experiments is then a simple matter invol-
ving just the HF elimination reaction, only the reaction’s
endothermicity together with its positive activation energy
requiring a computer model. Although it is sufficient to have
an initial gradient to set the rate in such a simple situation,
modeling of the entire profile serves to improve the extrapola-
tion to t = 0, and employs all the measured values. Computed
gradients that closely fit the experimental measurements are
shown as black solid lines in the figure.
interpreting the ST/TOF-MS data. Rate constants were ex-
tracted from concentration profiles by modeling the profiles
with the same code used to simulate the ST/LS experiments.
Here t = 0 is located as described in ref. 26 and 27 and the
solid lines in Fig. 12 show the result of the simulation.
The two channels, (2) and (3), produce identical products,
so only their sum can be observed. Electronic structure
calculations described in the Appendix also indicate nearly
identical barriers for these channels. Using the additional
theoretical parameters of Table 1, TST calculations then also
suggest equal kN for (2) and (3), with a sum kN = 6.0256 ꢃ
1014 exp(ꢀ76.344 (kcal molꢀ1)/RT). The RRKM falloff mod-
eling now uses only one of the two reactions, with one
activation energy, but with its rate parameters increased by
adjusting the reaction-path degeneracy to fit the sum of the
two.
Experimental total rate constants from both ST/LS and ST/
TOF-MS are shown in Fig. 13, together with the earlier single-
pulse experiments of Simmie et al.37 As expected, the experi-
ments show a fairly strong falloff at the higher temperatures.
One difficulty evident in Fig. 13 is a poor fit to the high-
pressure ST/TOF-MS and Simmie et al.37 rates, which are too
high throughout. Of course the agreement would be even
poorer with any reduction of either channel, suggesting a full
contribution of both channels to the thermal reaction, as is
indicated by the electronic structure calculations. As noted
earlier, Simmie et al.,37 do mention seeing some small quan-
tities of bond fission products in their GC analyses, and this
may well have caused some increased destruction of the parent
vinyl fluoride, leading to an increase in apparent rate.
However, there is another possible interpretation of the
above. The data in Fig. 13, all of it, can be seen as actually
The ST/TOF-MS experiments were conducted for reflected
shock pressures, P5, of 500–1300 torr and temperatures, T5, of
1500–1980 K. Fig. 2a shows a large increase in the peak
heights at around 300 ms which arises primarily from the
increasing pressure in the ion source following reflection of
the shock wave from the end wall of the driven section and is
accounted for with an inert internal standard, here argon.27,28
Vinyl fluoride fragments in the ion source and a mass spec-
trum, 30 eV electron energy, for pure vinyl fluoride are shown
in Fig. 11. The mass spectrum shows a small fragment at m/z =
26 which is equivalent to C2H2+. Consequently, the m/z = 26
peak area is corrected by 7% of the vinyl fluoride, m/z = 46,
peak area in each discrete mass spectrum to obtain the actual
concentration of C2H2 that arises from dissociation of vinyl
fluoride. From the individual mass spectra, see for example
ꢁc
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Table 1 RRKM models for reactions (2) and (3)
Molecular vibrational frequencies (cmꢀ1) and degeneracies
466(1), 705(1), 838(1), 914(1), 939(1), 1145(1), 1298(1), 1386(1), 1675(1),
3070(1), 3094(1), 3159(1).
Transition state vibrational frequencies (cmꢀ1) and degeneracies 241(1), 464(1), 560(1), 734(1), 812(1), 922(1), 1261(1), 1613(1), 2106(1),
(1,1-HF elimination)
3045(1), 3125(1).
Transition state vibrational frequencies (cmꢀ1) and degeneracies 505(1), 572(1), 666(1), 713(1), 735(1), 898(1), 980(1), 1623(1), 1759(1), 3210(1),
(1,2-HF elimination)
3276(1)
Moments of inertia (10ꢀ40 g cm2)
Molecular adiabatic:
Transition state adiabatic: (1,1-HF elimination)
Transition state adiabatic: (1,2-HF elimination)
Molecular active:
79.74, 92.53
112.13, 126.34
81.48, 101.17
12.79
Transition state active: (1,1-HF elimination)
Transition state active: (1,2-HF elimination)
Reaction path degeneracy: (1,1-HF elimination)
Reaction path degeneracy: (1,2-HF elimination)
14.21
19.69
1
1
67.28
23.65
74.19
DH0 (kcal molꢀ1): (1,1-HF elimination)
0
DH00(kcal molꢀ1): (1,2-HF elimination)
E0 (kcal molꢀ1): (1,1-HF elimination)
E0 (kcal molꢀ1): (1,2-HF elimination)
71.76
See captions to Fig. 13 and 14
2
hDEidown (cmꢀ1
)
Number of Morse oscillators
L-J collision parameters
Collision diametersc (angstroms)
e/k potential well depth (K)
CH2CHF: 4.2, Kr: 3.61
CH2CHF: 230, Kr: 178
quite consistently supporting a larger rate for kN than that
taken from the structure calculations. Assuming any failing in
these calculations would likely reside in the barriers, we have
shown in Fig. 14 the result of reducing the barrier of both
channels 2a and 3 (Table 2) to 70 kcal molꢀ1. The fit is seen to
be much improved throughout. We are certainly not suggest-
ing that the structure calculations are in this much error,
merely that the experiments are, in themselves, in better accord
with a lower barrier. Finally, the low-barrier RRKM fit in Fig.
14 has again a rather large hDEidown of 900 cmꢀ1, which choice
seems near optimal, but still does not produce a completely
satisfactory fit. This hDEidown is similar to, if perhaps some-
what larger than, what is seen in 1,1,1-trifluoroethane1 and the
present 1,1-difluoroethane described below. Unfortunately,
Fig. 13 Results from the ST/LS and ST/TOF-MS experiments for
vinyl fluoride dissociation comparing with the literature data and the
results of RRKM calculations. ST/LS experiments: 10% CHFQCH2/
Kr: [’] 75–140 torr, [K] 206–300 torr, [m] 311–482 torr; 4%
CHFQCH2/Kr, [v] 177–322 torr. ST-TOF/MS experiments: (4%
CHFQCH2 + 4%Ar)/Ne, [B] 516–633 torr, [J] 1210–1373 torr.
The lines illustrate RRKM calculations: 100 torr [--], 500 torr [-ꢄ-] and
3200 torr [ꢄ ꢄ ꢄ] using the parameters of Table 1 with E0 = 71.76 kcal
molꢀ1 (see Table 2). Here the collision efficiency, oDE4down
=
Fig. 14 RRKM calculations showing an optimized fit to the experi-
mental data for vinyl fluoride dissociation. Here, E0 has been lowered
by 1.5 to 70 kcal molꢀ1 and hDEidown = 900 cmꢀ1, the other
parameters for the RRKM calculations are as in Table 1. Here,
250(T/298)0.9 cmꢀ1, is chosen as a typical value. The heavy, steep line
at the top shows the summed kN for reactions (2) and (3) taken
directly from the TST calculations, again using the parameters in
Table 1. The rates obtained in the single-pulse experiments of Simmie,
et al. 37, are shown as [&] for their 2800–3600 torr range.
k
N = 6.0256 ꢃ 1014 exp(ꢀ73.505 (kcal molꢀ1)/RT). The experiments
and calculations are identified as in Fig. 13.
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Table 2 Energies from ab-initio calculations relative to C2H3F
(see appendix and Fig. 18)
G3B3/
kcal molꢀ1
HL1/
kcal molꢀ1
HL2/
kcal molꢀ1
Species
CH2QC: + HF
C2H2 + HF
TS2a
TS2b
TS3
65.29
21.65
74.51
66.9
65.49
22.38
74.36
65.98
72.56
64.73
21.56
74.19
65.43
71.76
72.94
our understanding of the origin of such empirical parameters
is still in a primitive state.
B. 1,1-Difluoroethane
Here ST/LS experiments were performed with mixtures of
10% difluoroethane in Kr and cover 1500–2000 K, for 43 o
P o 424 torr. The high concentration is necessary because of
the small heat of reaction. Fig. 15 exhibits the results of ST/LS
density gradients showing dissociation. As above, these ex-
periments are at higher pressures and higher temperatures
than the relaxation experiments, and the relaxation process
is lost in the shock-front signal. Modeling of these experiments
now involves just two reactions, the dissociation (1) and the
sum of the vinyl fluoride reactions (2) and (3), with rates taken
from the above study. At the beginning of the reaction,
elimination of HF from 1,1- difluoroethane is dominant, but
after about 2 ms, a small contribution from vinyl fluoride
begins as shown in Fig. 16. Computed gradients modeling the
experimental values are included as black solid lines in the
Fig. 16 An example ST/LS experiment on 1,1-difluoroethane dis-
sociation showing the separate contributions to the gradient from both
initial HF elimination (intermediate solid line) and subsequent vinyl
fluoride dissociation (lowest line). The line above both shows the total.
At the beginning the density gradient is entirely from difluoroethane
decomposition, but after about 2 ms, vinyl fluoride dissociation starts
to contribute.
figure. For this modeling only the magnitude and activation
energy of reaction (1) were varied.
Derived rate constants for (1) are now shown in Fig. 17,
together with the earlier single-pulse experiments of
Fig. 15 Example ST/LS dissociation gradients in 1,1-difluoroethane, DFE, [J], and modeling of these (solid lines), over a wide pressure range
from 43 to 424 torr. The inset has the usual semi-log plot of gradient obtained from the displayed raw signal. Here temperatures and pressures are
all vibrationally relaxed, chemically frozen, ideal post-incident shock values, values used at the start of the modeling shown as a solid line. Again,
the late distortions in the higher pressure experiments are ascribed to boundary layer effects.
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Fig. 18 Potential energy surface for the dissociation of vinyl fluoride
by reactions (2) and (3). Energy barriers are derived from G3B3
calculations (see text and Table 2).
Fig. 17 ST/LS rate constants for reaction (1), HF elimination in 10%
1,1-difluoroethane/Kr; [$] 43–52 torr, [K] 50–109 torr, [n] 311–
424 torr, with the experiments of Tschuikow-Roux, et al.,17 [&], for
2300–4000 torr. The lines illustrate RRKM calculations, 36 torr [--], 80
torr [-ꢄ-], 368 torr [ꢄ ꢄ ꢄ] and 3150 torr [—], using the parameters of Table
3. The collision efficiency, oDE4down =1600 cmꢀ1, was selected to
produce the fit shown. The heavy, steep line at the top displays kN
taken from the TST calculation using the parameters of Table 3. Here,
kN = 8.53 x 1014exp(ꢀ67.581 (kcal/mol)/RT).
conditions. In addition, the TOF experiments extend the
temperature range to lower temperatures and higher pressures,
and serve to confirm the prior notion that the dissociation of
vinyl fluoride is confined to HF elimination. For the two
channels of this reaction, (2) and (3), electronic structure
calculations find very similar barriers and high-pressure rate
constants. In both vinyl fluoride and 1,1-difluoroethane calcu-
lated kN are close in magnitude and activation energy to
earlier high-pressure measurements,17,37 although the calcu-
lated rates may be a bit low in vinyl fluoride. This latter
observation gives rise to the tentative suggestion that the
barriers obtained from the electronic structure calculations
for vinyl fluoride are slightly too high. Here the measured rate
data are actually consistent with a larger high-pressure rate
than is provided by the theory. Regardless of the choice of kN
Tschuikow-Roux, et al.,17 and these include the results of
RRKM calculations (discussed below). As expected, the ex-
periments show a small but clearly discernible falloff. However
here, in contrast to the trifluoroethane,1 falloff seems normal
and there is no sign of non-RRKM behavior.
As with vinyl fluoride, the RRKM model is derived from
G3B3 electronic structure calculations. These calculations
generate a TST kN(sꢀ1) = 8.53 ꢃ 1014 exp(ꢀ67.581 kcal
molꢀ1/RT), in superb agreement with the high-pressure mea-
surements of ref. 17, also shown in Fig. 17. The falloff seen in
the experiments does again indicate a rather large hDEidown of
1600 cmꢀ1, but this is similar to, if somewhat larger than, the
above, and not far from what was found in 1,1,1-trifluoro-
ethane.1
Table 3 RRKM model for reaction (1)
Molecular vibrational
frequencies (cmꢀ1) and
degeneracies
241(1), 363(1), 443(1), 544(1),
848(1), 936(1), 1106(1), 1133(1),
1133(1), 1360(1), 1371(1), 1404(1),
1457(1), 1460(1), 2955(1), 2960(1),
3031(1), 3034(1)
Discussion and conclusions
Transition state vibrational
frequencies (cmꢀ1) and
degeneracies
245(1), 396(1), 474(1), 549(1),
586(1), 848(1), 930(1), 994(1),
1193(1), 1230(1), 1251(1), 1392(1),
1511(1), 1603(1), 3044(1), 3111(1),
3134(1)
The present experiments and theory offer several conclusions.
Regarding vibrational relaxation, in both vinyl fluoride and
1,1-difluoroethane this is extremely rapid, with energy transfer
occurring on essentially a few collisions. The relaxation times
obtained by extrapolation for the pure vinyl fluoride agree well
with earlier ultrasonic results, and all the results are entirely
consistent with measurements on similar systems. The usual
difficulty with overly large integrated gradients also persists in
these cases; this may reflect inadequate time origin location, as
suggested before, or it may indicate non-exponential behavior
during the earliest unobservable few tenths of a microsecond.
In any case, the fast relaxation would certainly suggest that
incubation delays may be safely discounted in the dissociation
experiments.
Moments of inertia/10ꢀ40 g cm2
Molecular adiabatic:
Transition state adiabatic:
Molecular active:
93.59 163.41
118.36 182.41
89.65
87.67
6
23.19
64.39
1600
2
Transition state active:
Reaction path degeneracy:
DH0 (kcal molꢀ1):
0
E0 (kcal molꢀ1):
hDEidown (cmꢀ1
)
Number of morse oscillators
L-J collision parameters
Collision diametersc (angstroms) CHF2CH3: 4.45, Kr: 3.61
e/k potential well depth/K CHF2CH3: 240, Kr: 178
The vinyl fluoride dissociation experiments utilize both LS
and TOF techniques, with good agreement on rates for similar
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the energy transfer efficiency, hDEidown, is large, 900 cmꢀ1
,
cantly higher barriers. This is in agreement with prior detailed
theoretical studies on an analogous system, vinyl chloride,50
wherein the three-centered and four-centered HCl eliminations
have significantly lower barriers than other elimination chan-
nels. In general, the energies predicted by the three methods in
this work are in excellent agreement (within 1 kcal molꢀ1) as
can be seen in Table 2 which presents the zero point corrected
energies relative to vinyl fluoride and validates the barriers
used in subsequent kinetic modeling.
much greater than that usually found in earlier work on non-
fluorinated species,38,39 although similar to what was found in
1,1,1-trifluoroethane. It is hard to believe that the simple
introduction of fluorine would produce such an immense
change in hDEidown at dissociation energies. Is this some
obscure feature associated with molecular reaction? The ques-
tion certainly seems to indicate the need for further study.
Appendix
Acknowledgements
Ab initio electronic structure calculations were performed
using the Gaussian 0340 suite of programs. Input structures
were generated using CHEM3D, a part of the CHEMOF-
FICE41 suite of programs. MOLEKEL42 and gOPENMOL43
were used to visualize the minima and saddle points on the
PES.
This work was supported by the Office of Basic Energy
Sciences, Division of Chemical Sciences, Geosciences, and
Biosciences, US Department of Energy, under contract
DE-FE85ER13384, and DE-AC02-06CH11357.
Geometric structures and vibrational frequencies for the
minima and saddle points were obtained using density func-
tional theory utilizing the B3-LYP44 functional with the small
double-z 6-31G(d) basis set and the larger triple-z
6-311++G(d,p) basis set. Transition states were verified by
visualization of the imaginary frequency as well as by per-
forming intrinsic reaction coordinate (IRC)45 calculations.
Subsequent higher level energies were obtained at the
G3B346 level of theory utilizing the B3-LYP/6-31G(d) geome-
tries and two non-parameterized high level methods referred
to as HL1 and HL2 utilizing the larger basis set B3-LYP/6-
311++G(d,p) geometries. Appropriate scaling factors46,47
were utilized for the G3B3 and the HL1 methods to scale
the theoretically determined frequencies and zero point cor-
rected energies. HL1 and HL2 represent additivity approxima-
tions equivalent to QCISD(T,Full)/6-311+G(3df,2pd)//
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