Infrared emission accompanying the gas phase recombination of alkyl radicals

Article abstract of DOI:10.1039/b303780k

Infrared emission from nascent products of the methyl radical recombination reaction has been detected using time-resolved Fourier transform emission spectroscopy. Methyl radicals were generated by 193 nm photolysis of acetone, and at low pressures emission from nascent photofragments (CH₃ and CO) is found to dominate. At higher pressures an additional emission band is seen in the C-H stretching region, the time dependence of which shows a rapid rise and a slow decay, the latter being dependent on the laser intensity and accurately described by a second-order fit. The emission is assigned to vibrationally excited ethane formed by recombination of methyl radicals, with the decay identified as the recombination rate and the rapid rise as quenching of C₂H₆ to levels which have no excitation in the emitting mode (the ν₅ C-H stretch). The recombination rate constants were determined from fits to the decays together with measurements of the laser fluence, and agree well with previous determinations. The wavelength dependence of the C₂H₆ emission spectrum is invariant with time, and is always red-shifted with respect to a room-temperature C₂H₆ absorption spectrum. This can be rationalised in a model which recognises that formation of vibrationally excited C₂H₆ is considerably slower than quenching, and from which it is found that the average level of excitation per excited ethane molecule reaches a steady-state value after a short induction period. Similar spectra and kinetics were observed with other methyl radical sources, and emission from the products of the ethyl radical recombination/disproportionation reaction was also observed when diethyl ketone was photolysed at 193 nm.

Full text of DOI:10.1039/b303780k

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Infrared emission accompanying the gas phase recombination of alkyl
radicalsy
Gus Hancock,* Vanessa Haverd and Marc Morrison
Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road,
Oxford OX1 3QZ, UK
Received 4th April 2003, Accepted 30th May 2003
First published as an Advance Article on the web 18th June 2003
Infrared emission from nascent products of the methyl radical recombination reaction has been detected
using time-resolved Fourier transform emission spectroscopy. Methyl radicals were generated by 193 nm
photolysis of acetone, and at low pressures emission from nascent photofragments (CH3 and CO) is found to
dominate. At higher pressures an additional emission band is seen in the C–H stretching region, the time
dependence of which shows a rapid rise and a slow decay, the latter being dependent on the laser intensity and
accurately described by a second-order fit. The emission is assigned to vibrationally excited ethane formed by
recombination of methyl radicals, with the decay identified as the recombination rate and the rapid rise as
quenching of C2H6 to levels which have no excitation in the emitting mode (the n5 C–H stretch). The
recombination rate constants were determined from fits to the decays together with measurements of the laser
fluence, and agree well with previous determinations. The wavelength dependence of the C2H6 emission
spectrum is invariant with time, and is always red-shifted with respect to a room-temperature C2H6 absorption
spectrum. This can be rationalised in a model which recognises that formation of vibrationally excited
C2H6 is considerably slower than quenching, and from which it is found that the average level of excitation per
excited ethane molecule reaches a steady-state value after a short induction period. Similar spectra and kinetics
were observed with other methyl radical sources, and emission from the products of the ethyl radical
recombination/disproportionation reaction was also observed when diethyl ketone was photolysed
at 193 nm.
We report here spectral and kinetic evidence of infrared
Introduction
emission which accompanies the recombination of alkyl radi-
cals in the gas phase. We concentrate on methyl radicals
formed from the 193 nm photolysis of acetone:
The mechanism for recombination of atoms or molecules in
the gas phase to form a single stable species must include a
step in which the nascent adduct loses energy. This can take
place either by radiative or collisional processes. The most
commonly observed radiative processes are when an emitting
electronically excited state is formed either directly or via a
curve-crossing mechanism, and examples include the recombi-
natioꢀn of O(1D) and O(3P) atoms forming directly the O2
B3Su state, and the recombination of ground-state oxygen
and nitrogen atoms through inverse predissociation to form
the C2P state of NO.1 If the adduct is formed in its ground
electronic state, loss of vibrational energy by infrared radia-
tion can still act as the stabilisation mechanism, and such
steps have been invoked in processes ranging from low-pres-
sure ion-molecule reactions2 to alkyl radical recombination in
interstellar space.3 The more commonly observed stabilisation
process however is by collision. Here the initially formed
adduct, normally in its ground electronic state, is quenched
to levels which are below its dissociation limit, and although
these levels are kinetically stable with respect to redissociation
they possess considerable internal energy which has even-
tually to be lost to the surroundings. Collisional stabilisation
of the adduct necessarily means that collisional energy loss
can also take place, but where vibrational transitions in the
infrared are allowed they must concomitantly occur and
result in infrared emission.
CH3COCH3 þ hnð193 nmÞ ! 2 CH3 þ CO
ð1Þ
Reaction (1) is a clean source of CH3 , with a quantum yield
for formation of two methyl radicals close to unity (F ¼
0.95).4–6 Infrared emission,7–10 laser induced fluorescence
(LIF),11resonantlyenhancedmultiphotonionisation(REMPI),11
photofragment spectroscopy6 and diode laser absorption12
have all been used to study features of the photodissociation
dynamics, and the general consensus is that dissociation
takes place in a stepwise fashion following initial formation
of CH3CO and CH3 and subsequent decomposition of the
acetyl radical.6–8,12 The methyl fragment emits in the
C–H stretching region near 3050 cmꢀ1, and measurements of
its internal energy distributions and energy transfer rates of the
fragment have been inferred from the wavelength and time
dependences of the emission.7,9,13 Donaldson and Leone7
observed additional long-lived emission in the C–H stretch
region which they attributed to vibrationally excited acetone
formed by energy transfer, but suggested that its persistence
with the addition of Ar could be caused by a contribution from
the C–H stretch modes of C2H6 formed by methyl radical
recombination. Mohammed et al.9 reported the kinetic beha-
viour of emission above 3000 cmꢀ1, and suggested that a
long-time component could result from methyl radical recom-
bination. Neither of these studies provided other than qualita-
tive evidence of the recombination process. Here we observe
time-resolved Fourier transform infrared (FTIR) emission
y Electronic supplementary information (ESI) available: Appendix:
Model for emission from the C2H6 recombination product of CH3
radicals. See http://www.rsc.org/suppdata/cp/b3/b303780k/
DOI: 10.1039/b303780k
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This journal is # The Owner Societies 2003
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from methyl radicals in the C–H stretching region, together
with a spectrally and kinetically distinct emission feature which
is assigned to highly vibrationally excited ethane. We show
how the kinetics of the emission are consistent with this assign-
ment, and can be used to obtain pressure dependent recombi-
nation rate constants. Photolysis of other methyl radical
precursors produces the same features. In addition, we report
the kinetic and spectroscopic features of emission in the C–H
stretch region following 193 nm photolysis of diethyl ketone,
with emission seen from nascent ethyl radicals and from a
product of the recombination/disproportionation reaction of
two ethyl radicals.
Experimental
The technique of time-resolved FTIR using a step scan interfe-
rometer has been described in several reviews,14–16 and our
experimental arrangement17,18 is summarised here. Radiation
at 193 nm from an excimer laser (Lambda Physik Compex
102, 100 mJ pulseꢀ1, 10 Hz) entered a reaction vessel equipped
with Welsh cell optics in the infrared, either in a single pass or
multipassed with high reflectivity mirrors (see below). A small
number of experiments used radiation at 248 nm from the
same laser. Infrared emission was directed into a step scan
interferometer (Bruker IFS/66) and detected in most experi-
ments with an InSb (Graseby IS2) detector operating in the
range 2–5.5 mm and for experiments at longer wavelengths
(up to 10 mm) with a HgCdTe (Kolmar D317) detector. The
signal was amplified, digitised (12 bits typically at 1 ms inter-
vals) and averaged for a preset number of shots (typically
20) at each mirror position. A series of time traces as a func-
tion of mirror displacement was thus generated, and these were
processed to yield interferograms and thus spectra as a func-
tion of time.19 Spectral resolution was determined by the total
mirror displacement and ranged from 1 to 20 cmꢀ1, and
the time resolution was ꢁ2 ms, limited by the risetime of the
detector/amplifier combination.
Data for kinetic analysis were recorded at higher signal to
noise ratios with interference filters used to isolate spectral fea-
tures. For these measurements the multipass laser optics were
removed and laser fluences were kept sufficiently low (3–13 ꢂ
1015 photon cmꢀ2) to avoid any secondary dissociation.4 Acet-
one, CH3I, and diethyl ketone (all Aldrich, > 99.5%) were
degassed by freeze–thaw cycling; Ar (BOC > 99.999%) was
used without further purification. Pressures were measured
by a previously calibrated capacitance manometer (Data-
metrics Barocell 600A 10 Torr head).
Fig. 1 Emission in the 2000–4000 cmꢀ1 region observed following
the photolysis of acetone (15 mTorr) at 193 nm. Resolution 10 cmꢀ1
.
The band centred at 2141 cmꢀ1 is emission from CO (Dv ¼ ꢀ1) transi-
tions, and the time dependence shows evidence of the collapse of the
rotationally and vibrationally excited nascent CO to a room-tempera-
ture distribution in v ¼ 1. The prompt emission feature at 3100 cmꢀ1 is
assigned to CH3 (Dn3 ¼ ꢀ1) transitions.
be measured. A simulation of the emission spectrum expected
from radicals at a rotational temperature of 298 K excited
purely in n3 ¼ 1 is shown in Fig. 2, and features in the P
branch at 3100, 3110, 3120 and 3130 cmꢀ1 are discernable in
both the simulation and the data (the filter cutoff above 3150
cmꢀ1 precludes observation of the R branch emission for this
transition). The sharp features near 3040 cmꢀ1 are red-shifted
Results
1. 193 nm acetone photolysis: time-resolved emission spectra
Fig. 1 shows time-resolved emission spectra at low resolution
(10 cmꢀ1) from the 193 nm photolysis of a low pressure of
acetone (15 mTorr), from which emission from both CO and
CH3 photofragments can be readily identified. The band
centred at 2141 cmꢀ1 is emission from CO (Dv ¼ ꢀ1) transi-
tions and the prompt emission feature at 3100 cmꢀ1 is assigned
to CH3 (Dn3 ¼ ꢀ1) transitions. The width of the CO band at
early time is indicative of high rotational excitation and the
earliest time data (2–3 ms corresponding to about 0.5 collisions
at 15 mTorr) are well represented by a simulated CO spectrum
using an internal energy distribution taken from previous
FTIR emission8,10 and LIF11 measurements. Part of the band
near 3100 cmꢀ1 is shown at higher resolution (1 cmꢀ1) in Fig. 2.
Here we are able to see persistent features which corre-
spond to partially rotationally resolved emission lines in the
CH3 Dn3 ¼ ꢀ1 band, but signal to noise ratios under these
conditions did not permit a nascent internal distribution to
Fig. 2 Emission in the region 2850–3150 cmꢀ1 at 1 cmꢀ1 resolution
from the photolysis of 25 mTorr acetone at 193 nm, summed between
5 and 40 ms after photolysis. An optical filter with a rapidly decreasing
transmission above 3150 cmꢀ1 was used in these experiments, and the
spectrum (a) has been corrected for the filter transmission. A simula-
tion, (b), at 1 cmꢀ1 resolution is also shown for CH3 n3 ¼ 1 ! 0 emis-
sion in this region, with features in the P branch matching those seen in
the data. The sharp features near 3040 cmꢀ1 have not been assigned,
but appear to be from methyl radicals with energies above that corre-
sponding to one quantum in the emitting mode n3 . The 2s noise level
in these experiments is measured as 5% of the maximum emission
intensity seen in Fig. 2.
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from the simulation, and correspond to transitions from radi-
cals with energies higher than simply a single quantum in n3
and which survive the average of five gas kinetic collisions
appropriate to this time window. We note that vibrational
excitation in the methyl fragment was inferred from the fre-
quency shift of the original low-resolution emission spectra
of Donaldson and Leone.7 Data were also acquired at lower
wavenumbers with the HgCdTe detector (1100–2000 cmꢀ1
)
and these showed only slowly rising bands at 1212, 1362,
1423 and 1735 cmꢀ1 which overlapped exactly with an absorp-
tion spectrum of acetone, were removed by a cold gas filter
containing acetone and were assigned to emission from vibra-
tionally excited acetone formed by energy transfer.
Fig. 3 shows time-resolved emission spectra in the C–H
stretching region, obtained at a higher pressure of acetone
(52 mTorr). In addition to emission from the CH3 photofrag-
ment as seen in Fig. 1, there is a feature centred at 2900 cmꢀ1
which grows in as the CH3 emission decays. This band has a
wavelength dependence which is independent of time and is
not removed to any significant degree by a cold gas filter of
acetone or of ethane. We assign this emission to Dn5 ¼ ꢀ1
transitions of highly vibrationally excited ethane formed by
CH3 recombination, and we present the evidence for this
below.
Fig. 4 Time dependence of the emission passed by a filter centred at
2926 cmꢀ1, FHWM ¼ 900 cmꢀ1 for two values of the laser fluence, 5.2
and 11.0 ꢂ 1015 photon cmꢀ2, for an acetone pressure of 34 mTorr in
the presence of 2 Torr Ar. The lower fluence trace has been multiplied
by a factor of four to equate the intensities of the second peaks.
as arising from CH3 (Dn3 ¼ ꢀ1) formed as a nascent product
from acetone photolysis. The height of this peak scales linearly
with the photolysis fluence, as shown in Fig. 5. The magnitude
of the second peak shows a greater than linear dependence on
the laser fluence, and its decay is fluence dependent. Fig. 4
illustrates this point. Here the signals for laser fluences differ-
ing by a factor of two are scaled to make the intensities of
the second peaks at ꢁ30 ms the same in order to emphasise
the observation that the decay rate increases with increasing
laser fluence, and to do this scaling the lower fluence trace
was multiplied by a factor of four. If we recall that a doubling
of the laser fluence increases the first peak height by a factor of
two (as shown in the data of Fig. 5), it can be seen that the flu-
ence dependence of the second peak must be more than linear
(approximately quadratic), and this is illustrated in Fig. 5.
Emission intensities taken in the multipass cell were larger
and showed better signal to noise ratios, but different kinetic
behaviour, than those found under single pass conditions at
the same fluence measured at the entrance window of the cell.
This is because the multipass cell has a spatially varying flu-
ence, caused by 193 nm photon loss both by acetone absorp-
tion and by losses on the multipass mirrors. Different
2. Time dependence of emission in the C–H stretching region
In Fig. 4 we show the time dependences of the emission passed
by an interference filter centred at 2926 cmꢀ1, FHWM ¼ 900
cmꢀ1 for two values of the laser fluence. In these experiments
we have added 2 Torr Ar to the mixture to minimise effects of
laser heating. From Fig. 3 it can be seen that the filter will pass
contributions from both emission features in the C–H stretch
region, and we see two distinct peaks in the time-resolved data
of Fig. 4. The first peak has its rise time determined by the
detector and amplifier time constant (2 ms), and we identify this
Fig. 3 Emission spectrum in the 2600–3400 cmꢀ1 region (5 cmꢀ1
resolution) following the 193 nm photolysis of 52 mTorr acetone. In
addition to the rapidly rising and falling nascent CH3 peak centred
at 3050 cmꢀ1 and seen in Fig. 1, there is an additional feature that
appears with slower kinetics at 2900 cmꢀ1, and is assigned as emission
from C2H6 formed by methyl radical recombination. The small dip in
the emission spectrum at 2970 cmꢀ1 is caused by non-resonant acetone
absorption in the Welsh cell.
Fig. 5 Measurements of the heights of the first (open triangles D) and
second (filled squares L) peaks such as those shown in Fig. 4 as a func-
tion of laser fluence I0 . 34 mTorr acetone, 2 Torr Ar. The straight line
is a least squares fit through the data for the first peak: the second peak
shows a more than linear dependence on laser fluence.
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fluences produce different decay rates of the signal (see Fig. 4),
and hence the decay under multipass conditions will be a con-
volution of signals over a non-uniform fluence distribution. All
kinetic data for analysis were thus taken under single pass
conditions such that the laser fluence was constant to within
experimental error.
The time-resolved data shown in Fig. 4 are of sufficient qual-
ity to show that the decay of the signal following the second
peak was not exponential, but could be accurately described
at longer times by second-order kinetics. This evidence,
together with the fluence dependences, is consistent with the
second peak being from a product of the recombination of
CH3 radicals, with the decay of the signal representing the
recombination step, and the rise (convoluted in Fig. 4 with
the fall of the CH3 emission signal) being the faster quenching
step of the vibrationally excited product. Methyl recombina-
tion forms exclusively C2H6 close to room temperature (dis-
proportionation is negligible)20 and we therefore identify
vibrationally excited ethane as the carrier of the emission near
2900 cmꢀ1. The fluence dependent decay rate (being propor-
tional to [CH3]2) is accounted for, and as the C2H6 quenching
rate is expected to be fluence independent it implies a more
than linear increase of the height of the second peak with flu-
ence. We note (see below) that we observe the same long-lived
emission from other photolytic methyl radical sources.
We now proceed to fit the time dependences of data such as
those in Fig. 4, with the main aims of demonstrating that the
second peak is kinetically consistent with its carrier being
C2H6 formed by methyl recombination, and of extracting the
recombination rate constant. First, a simple kinetic model
was proposed to describe the time evolution of the observed
emitting species, C2H6* and CH3*:
Fig. 6 Time dependence of the emission passed by the filter centred
at 2926 cmꢀ1: 34 mTorr acetone, 2 Torr Ar, I0 ¼ 1.2 ꢂ 1016 photon
cmꢀ2. The solid line is the experimental trace, the dotted line the fit
to the data as explained in the text.
which is not described by a single rate constant k2 . We also
ignore cascade of population through the vibrationally excited
C2H6 levels, and return to this point later. What however
should be noted is that the decay of the second peak is fitted
well, and inspection showed that this decay is representative
of the recombination process (3). Modifications to the model
were introduced to correct for the assumptions that all CH3
was produced with excitation in n3 and that removal of the
observed CH3* resulted exclusively in the formation of CH3
(v ¼ 0). These modifications improved the fit to the first peak,
unsurprisingly as more kinetic variables were introduced, but
more importantly the fit to the fall and the parameter of inter-
est, k3[CH3]0 , were robust to these modifications, giving us
confidence in the original simple model for the purpose of
fitting the slow decay of the second peak.
ꢃ
ðCH3Þ2CO þ hn ð193 nmÞ ! 2CH3 þ CO
ð1Þ
ð2Þ
k2
ꢃ
CH3 þ M
CH ðv ¼ 0Þ þ M
ƒƒƒ!
3
k3
ꢃ
CH ðv ¼ 0Þ þ CH ðv ¼ 0Þ
C H
2 6
ð3Þ
ð4Þ
ƒƒƒ!
3
3
Experiments were carried out to test the model by measuring
kinetics as a function of 193 nm laser fluence I0 (photon cmꢀ2
k4
ꢃ
C2H6 þ M
C H ðn ¼ 0Þ þ M
ƒƒƒ!
2
6
5
)
for a fixed pressure of acetone (34 mTorr) in Ar (2 Torr). The
fluence was estimated with a calibrated energy meter and with
careful measurements of the beam size in the cell, and this,
coupled with the absorption cross section of acetone at 193
nm ((2.1 ꢄ 0.2) ꢂ 10ꢀ18 cm2 21) allowed the initial concentra-
tion of methyl radicals [CH3]0 to be estimated with an accuracy
of 20% and over a fourfold range of concentration. The fitted
values of k3[CH3]0 vary linearly with [CH3]0 , as shown in
Fig. 7. The slope of the plot is (4.2 ꢄ 0.9) ꢂ 10ꢀ11 cm3
moleculeꢀ1 sꢀ1 and corresponds to the CH3 recombination
rate constant, k3 , at the pressure (34 mTorr acetone, 2 Torr
Ar) and temperature (295 K) used in this experiment.
The error reflects the uncertainty in the calculated value
The model assumes that the entire initial concentration of
methyl, [CH3]0 , is formed with vibrational excitation in n3 .
The vibrationally excited species, CH3*, gives rise to the first
peak in Fig. 4 and decays with a rate constant k2 to form
CH3 in the vibrational ground state (CH3 (v ¼ 0)) in collisions
with M (either acetone or argon). CH3 (v ¼ 0) recombines to
form the second emitting species, C2H6*, at a rate k3-
[CH3 (v ¼ 0)]2, where k3 is the second-order pressure depen-
dent rate constant. Thus, in addition to defining the decay rate
of the first peak, k2 also defines the rate at which CH3*
becomes available for recombination. C2H6* is the observed
vibrationally excited ethane recombination product, which
emits in Dn5 ¼ ꢀ1 transitions and is quenched by M with a
rate constant k4 to C2H6 (n5 ¼ 0). The modelled emission
intensity was multiplied by a function, f ¼ (1ꢀexp(ꢀt/t)), in
order to account for the t ¼ 2 ms electronic rise time, and
the rate equations for processes (2), (3) and (4) were solved
numerically using the Facsimile2 chemical modelling soft-
ware. The parameters which control the rate processes are k2
and k4 , the quenching rate constants for CH3 and C2H6 ,
respectively, and the product k3[CH3]0 (reflecting the second-
order nature of the recombination step) and these were varied
to obtain the best fit to the experimental data. An example of
such a fit is shown in Fig. 6. The model is necessarily a simpli-
fication: we ignore cascade of vibrational population in
CH3 (n3) which shifts the peak of the of the emitting species
slightly to the blue as time progresses (this can just be seen
in the early time data of Fig. 1), and will result in quenching
Fig. 7 Plot of the fitted values of the product k3[CH3]0 to the decay
of the emission such as that shown in Fig. 6 as a function of [CH3]0 ,
the latter being calculated from the measured fluence I0 at 193 nm.
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of [CH3]0 – statistical errors from the fits are considerably
smaller. A fall-off curve was obtained from data taken at a
value of I0 ¼ 8.3 ꢂ 1015 photon cmꢀ2 and over the pressure
range 0.5–8.0 Torr Ar for a fixed pressure of 55 mTorr acet-
one. The lower pressure limit of 0.5 Torr Ar was required to
avoid a significant temperature rise in the cell and to prevent
loss by diffusion on the time scale of the experiment. The
results are shown in Fig. 8 together with data reported by Sla-
gle et al.22 and Walter et al.23 and agree very well with these
previous measurements.
3. Other sources of alkyl radicals: methyl iodide and diethyl
ketone photolysis
We have observed emission from alkyl radical recombination
using other sources of alkyl radicals. Acetone photolysis at
248 nm showed emission with the same long-time characteris-
tics as for photolysis at 193 nm, but with considerably lowered
intensity (the absorption cross section is a factor of 20 lower).
Methyl iodide photolysis at 248 nm resulted in intense emis-
sion peaking at 2900 cmꢀ1, the long-time spectrum of which
was identical to that from acetone except for an additional
shoulder on the high wavenumber side, thought to be from
an energy transfer process to the parent molecule and which
prevented accurate determination of the decay kinetics. Fig. 9
shows time-resolved emission spectra in the C–H stretching
region for the 193 nm photolysis of diethyl ketone:
Fig. 9 Emission as a function of time following the 193 nm photoly-
sis of diethyl ketone (60 mTorr). The prompt double peaked feature is
assigned to emission from nascent C2H5 radicals, and this is replaced at
longer times by a feature near 2900 cmꢀ1, the kinetic behaviour of
which is consistent with the carrier being formed from the reaction
of two ethyl radicals.
C2H5COC2H5 þ hnð193 nmÞ ! 2 C2H5 þ CO
ð5Þ
Prompt emission is seen from vibrationally excited C2H5 which
has fundamental frequencies ranging from 2840 to 3112
cmꢀ1 24
and this is followed by a slowly decaying feature,
,
which again does not shift in wavelength with time. It is
assigned to C–H vibrations from products of recombination
and disproportionation of ethyl radicals:
hence I0), indicating again that the longer time emission is
indeed from a product of a radical–radical reaction. The slope
of this plot gives a rate constant k6 for C2H5 self-reaction at
p(Ar) ¼ 0.400 Torr of (1.31 ꢄ 0.26) ꢂ 10ꢀ11 cm3 moleculeꢀ1
k6
C H þ C H þ M
products
ð6Þ
ƒƒƒ!
2
5
2
5
s
ꢀ1, with the quoted error including uncertainties in the slope
The recombination (to C4H10)/disproportionation (to
C2H6 + C2H4) ratio is 7 : 1 at low temperatures,20 but the
broad nature of the spectrum precludes a definite identification
of the dominant emitter. The mechanism however was con-
firmed by fitting the decay of the band as a function of I0 in
the same way as the acetone data were fitted. The results are
plotted in Fig. 10 and, as for the CH3 recombination data,
the fitted values of k6[C2H5]0 vary linearly with [C2H5]0 (and
and in the measurement of [C2H5]0 . The limiting high-pressure
rate constant for reaction (6) is recommended to be 1.9 ꢂ 10ꢀ11
cm3 moleculeꢀ1 sꢀ1 20
and recent cavity ring down (CRD)
,
measurements of the loss rate of the radicals in 5.6 Torr Ar
show that it appears to have reached the limiting value at that
pressure.25 Our measurement at 0.4 Torr is within the error
bars of the CRD value of (1.99 ꢄ 0.44) ꢂ 10ꢀ11 cm3 moleculeꢀ1
s ,
ꢀ1 25 but we need to consider if our lower value indicates that
the high-pressure limit is not reached at 0.4 Torr. A surprising
result from room temperature very low pressure pyrolysis
experiments carried out at 3 mTorr shows that although the
Fig. 10 Plot of the fitted value of k6[C2H5]0 against [C2H5]0 taken
from fits to the long-time behaviour of the emission near 2900 cmꢀ1
seen following the photolysis of diethyl ketone (100 mTorr) in Ar
(400 mTorr). The slope yields a value for the rate constant of the
C2H5 recombination/disproportionation reaction of (1.3 ꢄ 0.26) ꢂ
Fig. 8 Plot of the fall-off curve for the recombination rate constant
k3 as a function of pressure of Ar. Filled triangles / with error bars
are from the present data, and the open squares K and circles X
are from the measurements of Slagle et al.22 and Walter et al.,23
respectively.
10ꢀ11 cm3 moleculeꢀ1 sꢀ1
.
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disproportionation rate constant is in agreement with the
accepted value measured at higher pressures, the recombina-
tion rate is negligible, despite an RRKM calculation showing
that even at 3 mTorr it should be at its high-pressure limit.26
We simply conclude that our measured value is kinetically
consistent with the identification of the long-time emission
following 193 nm photolysis of diethyl ketone as resulting
from the products of reaction (6).
account for the lack of observed spectral shift. We note that
we have identified a production process of C2H6* which is
slower than its quenching. Steady-state approximations clearly
do not apply to the concentrations of the emitting molecules,
but the invariance of the spectrum with time suggests that this
might be so for the average energy. The details of the model
are given in the Appendix which is provided as supplementary
electronic material.y Briefly, we construct a ladder of C2H6
states dependent only upon total energy, and allow collisional
transfer into and out of these levels which take place in either
a mode specific fashion, removing a quantum in the emitting
n5 mode, or in an energy specific fashion, taking out energy
in the remaining modes. Mode specific rate constants are derived
from the C2H6* emission profiles such as those in Fig. 6:
energy specific rate constants are assumed to be gas kinetic
with the amount of energy removed per collision depending
upon both collision partner and total energy.27,28 From these
data we calculate an average internal energy hEi in the C2H6
molecule as a function of time after acetone photolysis.
Results show that under conditions such as shown in Fig. 1
the value of hEi rapidly drops (in about 30 ms) from the initial
31 300 cmꢀ1 to a value of ca. 21 000 cmꢀ1, which then remains
constant for the time scale of the experimental observations,
i.e. the value of hEi appears to reach a steady state. Addition
of Ar (the simulation was run at an Ar pressure of 8 Torr,
the maximum used in the kinetic measurements) caused the
steady state to be reached in a shorter time scale, and hEi to
decrease to 14 000 cmꢀ1. A steady state value of hEi is consis-
tent with the invariance of the emission spectrum with time,
and in the induction period the C2H6 molecules with higher
hEi (the emission from which would be expected to be red-
shifted with respect to the steady-state spectrum) will be at
low concentrations and masked by the short lived emission
from CH3 .If we assume that an internal energy of 21 000
cmꢀ1 corresponds to an anharmonic shift of 25 cmꢀ1 (since
the observed emission at 2900 cmꢀ1 is red-shifted by ꢁ25
cmꢀ1 compared to the feature in the C2H6 absorption spec-
trum) and that this shift decreases linearly with the internal
energy of the emitter, then we predict that, with 8 Torr of
added Ar, the emission would be centred at 2908 cmꢀ1. We
observe no difference in the spectral distribution of the C2H6
emission recorded with and without 8 Torr Ar at a resolution
of 10 cmꢀ1. This does not contradict results of the model since
the low resolution, combined with the broad, unstructured nat-
ure of the emission would make a shift of 8 cmꢀ1 in the mean
emission frequency difficult to observe. The simple model is
thus able to account for the observations, and indicates that
a steady state of internal energy can be reached in an ensemble
of molecules whose total population is changing with time.
Discussion
1. Comparison with previous assignments
There have been previous reports of late-time emission in the
C–H stretching region following photolysis of acetone and
diethyl ketone. In their low-resolution (30–60 cmꢀ1) study of
193 nm acetone photolysis, Donaldson and Leone7 suggested
that emission in the 2800–3400 cmꢀ1 region was predomi-
nantly from CH3 (Dn3 ¼ ꢀ1), with weak emission from acet-
one appearing at longer times, consistent with energy
transfer from CH3 to acetone. In the presence of Ar, the late
time emission was assigned to vibrationally excited ethane
from CH3 recombination, rather than acetone since, in this
case, deactivation of CH3 (n3 ꢅ 1) by Ar competed with vibra-
tional energy transfer to acetone. We agree with the CH3 and
C2H6 assignments, but our results suggest that the weak long-
lived emission in the absence of Ar is also from ethane: we see
no resonant absorption by a cold gas filter containing acetone,
and for a wide variety of fluences and pressures we find that
the emission is described by second-order kinetics rather than
an exponential decay as expected from energy transfer.
Furthermore we find that the spectral distribution is unaffected
by Ar, consistent with the emitter being the same with and
without added Ar. Hall et al.10 studied the 193 nm photolysis
of acetone and diethyl ketone by time-resolved FTIR emission
spectroscopy. In the diethyl ketone study, emission near 2950
cmꢀ1 was assigned to C–H stretching vibrations of the ethyl
radical. The band, spanning 2800–3400 cmꢀ1, revealed no line
structure, even at 0.3 cmꢀ1 resolution. The study did not
include a quantitative kinetic analysis, although an initial rapid
decay and a slower decay at longer times were observed, just as
in the present experiments (Fig. 9). The rapid decay of the
emission was attributed to collisional redistribution of energy
out of the high frequency C–H modes. The slower decay at
longer times was attributed again to C2H5 , but now with the
loss of the emitting ethyl radicals being dominantly by recom-
bination/disproportionation. Our spectral results (Fig. 9) sug-
gest that there are two species emitting in the 2800–3400 cmꢀ1
region, and by analogy with the results for recombination of
CH3 radicals we would identify the species seen at later times
as a product of the C2H5 self-reaction.
Conclusions
2. Wavelength independence of the CH3 recombination band
The C2H6 (Dn5 ¼ ꢀ1) emission was unaffected by a cold gas
filter of ethane, and it is red-shifted by approximately 25
cmꢀ1 relative to the C–H stretching bands in the ethane
absorption spectrum. These observations indicate that the
emitting species is highly vibrationally excited, as expected
from the highly exothermic methyl recombination reaction
Infrared emission which accompanies the 193 nm photolysis of
acetone has been shown to arise both from nascent photofrag-
ments, and from C2H6 produced by recombination. Fits to
the slow decay of the emission have shown that this corresponds
to the rate of recombination of methyl radicals, and rate con-
stants thus obtained are consistent with previous measure-
ments. The observations indicate a straightforward way of
rapidly obtaining good signal-to-noise fall-off data at low pres-
sures for alkyl recombination reactions, with the dominant
source of uncertainty (as in most recombination measure-
ments) being the determination of the initial radical concentra-
tion. The emission from C2H6 is not affected by vibrational
cascade (i.e. there is no spectral shift with time) and we show
that this lack of spectral shift is attributable to slow production
and rapid collisional quenching of the emitting species. Similar
recombination spectra are seen with other CH3 radical sources,
0
(DH0 ¼ ꢀ31 300 cmꢀ1). The vibrational energy in excess of
the ground-state energy is removed by collisions with bath
gas molecules and, as the emitting species loses energy, the
anharmonic shift decreases. We might therefore expect the
emission to shift to higher wavenumber with time. However,
as seen in Fig. 1, the spectral distribution of the
C2H6 (Dn5 ¼ ꢀ1) emission is invariant with time, and this
was found to be the case under all experimental conditions.
Here we describe the results of a model of the time dependence
of the internal energy of the emitting species in order to
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Phys. Chem. Chem. Phys., 2003, 5, 2981–2987

View Article Online
12 G. E. Hall, D. Van den Bout and T. J. Sears, J. Chem. Phys., 1991,
94, 4182.
and the photolysis of diethyl ketone yields data for the recom-
bination/disproportionation reaction of two ethyl radicals.
13 D. J. Donaldson and S. R. Leone, J. Phys. Chem., 1987, 91, 3128.
14 S. R. Leone, Acc. Chem. Res., 1989, 22, 139.
15 J. J. Sloan and E. J. Kruus, in Advances in Spectroscopy: Time-
resolved Spectroscopy, ed. R. J. H. Clark and R. E. Hester, Wiley,
Chichester, 1989.
Acknowledgements
16 G. Hancock and D. E. Heard, Adv. Photochem., 1993, 18, 1.
17 C. Breheny, G. Hancock and C. Morrell, Phys. Chem. Chem.
Phys., 2000, 2, 5105.
We are grateful to the EPSRC and Bruker Instruments for
support of this work.
18 C. Breheny, G. Hancock and C. Morrell, Z. Phys. Chem., 2001,
215, 305.
19 P. Biggs, G. Hancock, D. E. Heard and R. P. Wayne, Meas. Sci.
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