Specific rate constants for the fragmentation of vibrationally excited benzyl radicals

Article abstract of DOI:10.1039/a806219f

The competition between collisional deactivation and fragmentation of vibrationally highly excited benzyl radicals in the ground electronic state has been investigated. Vibrationally highly excited benzyl radicals have been prepared from the dissociation of ethylbenzene after UV photon excitation followed by rapid internal conversion. Subsequently, the benzyl radicals are collisionally deactivated in collisions with the bath gas, argon. After selected delay times the benzyl radicals were excited again by absorption of another UV-photon, followed by fast internal conversion. A certain fraction of the reexcited benzyl radicals decomposes while the rest is collisionally stabilized. The total loss of benzyl radicals due to reexcitation has been monitored by UV absorption spectroscopy. Absolute values of the specific rate coefficients for fragmentation have been derived for excitation energies between 47000 and 53000 cm^-1. These specific rate constants agree well with a deconvolution of the thermal high pressure rate constant obtained from previous shock wave experiments.

Full text of DOI:10.1039/a806219f

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SpeciÐc rate constants for the fragmentation of vibrationally excited
benzyl radicals
M. Damm, F. Deckert, H. Hippler* and G. Rink
L ehrstuhl f ur Molekulare Physikalische Chemie, Institut f ur Physikalische Chemie und
Elektrochemie der Universitat Karlsruhe, Kaiserstrasse 12, D-76128 Karlsruhe, Germany
Recei¿ed 6th August 1998, Accepted 7th September 1998
The competition between collisional deactivation and fragmentation of vibrationally highly excited benzyl
radicals in the ground electronic state has been investigated. Vibrationally highly excited benzyl radicals have
been prepared from the dissociation of ethylbenzene after UV photon excitation followed by rapid internal
conversion. Subsequently, the benzyl radicals are collisionally deactivated in collisions with the bath gas,
argon. After selected delay times the benzyl radicals were excited again by absorption of another UV-photon,
followed by fast internal conversion. A certain fraction of the reexcited benzyl radicals decomposes while the
rest is collisionally stabilized. The total loss of benzyl radicals due to reexcitation has been monitored by UV
absorption spectroscopy. Absolute values of the speciÐc rate coefficients for fragmentation have been derived
for excitation energies between 47000 and 53000 cm~1. These speciÐc rate constants agree well with a
deconvolution of the thermal high pressure rate constant obtained from previous shock wave experiments.
internal conversion, thus avoiding the complications of a high
temperature environment and complications due to fast sub-
sequent reactions.
Introduction
Benzyl radicals play an important role in many combustion
processes. In particular, they are produced in the pyrolysis of
alkyl substituted benzenes such as toluene1h8 and ethyl-
benzene.9,10 However, under these pyrolytic conditions benzyl
radicals are not stable and will decompose. The fragmentation
of benzyl radicals has been the subject of many investiga-
tions.2h4,7h13 Mostly, benzyl radicals have been prepared by
thermal decomposition of an appropriate precursor in shock
waves. However, it has been difficult to directly measure the
subsequent thermal dissociation rate of benzyl radicals
because of the interference with consecutive reactions. Never-
theless, the thermal dissociation rate constant of benzyl rad-
icals has been extracted from modeling UV-absorptionÈtime
proÐles.
The basic idea of the presented experiment is illustrated in
Fig. 1. As shown in refs. 14 and 15, benzyl radicals can effi-
ciently be prepared from 193 nm photo-excitation of ethyl-
benzene which, after a fast internal conversion, decomposes in
a unimolecular reaction into vibrationally highly excited
benzyl radicals in the ground electronic state. The vibra-
tionally excited benzyl radicals can then be excited further by
single UV-photon absorption at 308 nm. Excitation can be
achieved immediately after their formation or after a selected
delay time when some energy has been lost in collisions with
inert bath gas molecules (Fig. 1). In any case, the electronically
excited benzyl radicals undergo fast internal conversion to the
ground electronic state. Thus, the internal energy of the benzyl
radicals in the electronic ground state can be varied over large
ranges by varying the delay time between the two laser pulses
or the bath gas pressure, and thus the number of deactivating
collisions, before excitation at 308 nm.
It has been shown that the rate of the disappearance of
benzyl radicals is identical to the rate of formation of hydro-
gen atoms,11 corresponding to a 1 : 1 ratio of benzyl loss to
hydrogen atom gain. Therefore, it has been suggested that the
rate determining step in the benzyl radical (C H ~) decomposi-
The fate of the benzyl radical is controlled by the com-
petition between unimolecular decomposition and bimolecu-
lar collisional deactivation, as illustrated also in Fig. 1. For a
7
7
tion is the elimination of a hydrogen atom, leaving a C H -
7
6
fragment behind. This is strongly supported by the detection
of C H -fragments of yet unknown structure by mass spec-
given total pressure the quantum yield of fragmentation, U ,
7
6
F
trometry in a molecular beam study of the unimolecular
decomposition of benzyl radicals.12 In addition, a recent
quantum chemical calculation of the potential energy
surface13 conÐrms this pathway. Thus we formulate the
thermal decomposition of benzyl radicals as a unimolecular
reaction:
increases with the initial excitation energy as schematically
shown. The characteristic shape of the curve is due to the
strong increase of the speciÐc rate constant for fragmentation
k(E) with increasing internal excitation energy (E) of the
benzyl radical while the rate constant of collisional deactiva-
tion k [M] depends only weakly on the excitation energy. As
D
the rate constant for collisional deactivation k has already
C H ~ ] M ] C H ] H~ ] M
(1)
D
7
7
7 6
been determined in separate experiments15 the speciÐc rate
constants for unimolecular decomposition k(E) can be deter-
for which the following Arrhenius expression in the high pres-
sure limit at temperatures between 1500 and 1800 K has been
given in ref. 7:
mined from the fragmentation yield U . From the dependence
F
of the fragmentation yield U (t ) on the delay time t between
F d
d
the two laser pulses, i.e. on the number of deactivating colli-
sions, the energy dependence of k(E) can be deduced. These
speciÐc rate constants are directly related to the thermal disso-
ciation rate constant in the high pressure limit.
k
(T ) \ 4.1 ] 1015 exp([350 kJ mol~1/RT ) s~1 (2)
1, =
In this paper we present a study of the fragmentation of
benzyl radicals after UV photoexcitation followed by fast
Phys. Chem. Chem. Phys., 1999, 1, 81È90
81

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U (P) \ [1 ] 2.4 ] 10~2 ] P(Ar)/mbar]~1
(3)
B
(ii) The simultaneously produced methyl radicals from the
dissociation of ethylbenzene have their absorption maximum
near 216 nm,31 are completely transparent at 253 nm, and so
do not e†ect the absorptionÈtime proÐles at the analysis
wavelength.
(iii) Ethylbenzene32 and methyl radicals31 essentially do not
absorb at 308 nm so that the second laser pulse only excites
benzyl radicals. The excitation wavelength of 308 nm guar-
antees that no additional benzyl radicals are formed from
excitation of the ethylbenzene molecules because of the low
absorption cross section for ““coldÏÏ and vibrationally excited
ethylbenzene molecules.
(iv) The concentration of initially formed benzyl radicals
c (P) at the total pressure P can easily be calculated from the
0
concentration of ethylbenzene [c(etb)], the quantum yield for
benzyl formation U (P) [see eqn. (3)], the absorption cross
B
section at the photolysis wavelength [e(193 nm) \
(1.9 ^ 0.1) ] 10~17 cm2, ref. 10], and the Ñuence of the 193
nm photolysis laser [F (193 nm)].
l
c (P) \ U (P)c(etb)
0
B
] M1 [ exp[[e(193 nm) ] F (193 nm)]N
(4)
l
Under typical conditions of F (193 nm) \ 3 mJ cm~2 and at a
l
total pressure of 4 mbar argon about 5% of the ethylbenzene
(typically 0.03 mbar) were converted into benzyl radicals.
These benzyl radicals are vibrationally excited. However, they
do not have enough energy to decompose and in time they are
all collisionally deactivated by the surrounding bath gas mol-
ecules.
(v) After a selected delay time the benzyl radicals are reex-
cited by absorption of a UV-photon at 308 nm and fast inter-
nal conversion into the ground electronic state follows. These
radicals may now be sufficiently vibrationally excited that
unimolecular decomposition can compete with collisional
deactivation.
Fig. 1 Scheme for the preparation of vibrationally highly excited
benzyl radicals by UV-multiphoton excitation. The excitation energy
of the benzyl radicals can be controlled by changing the number of
collisions before absorption of the 308 nm photon (see text). The
quantum yield shown for fragmentation (U ) depends on the inert gas
F
pressure and varies with the internal energy of the benzyl radicals.
Experimental
The benzyl radical is especially well suited for the experiments
presented here because of its particular photophysical proper-
ties. The optical transitions from the electronic ground state
(12B ) to the two lowest doublet states (12A , 22B ) near 450
The experimental setup is identical to that described in a
recent paper on the collisional energy transfer of benzyl
radicals15 and therefore will be mentioned only brieÑy. Excita-
tion light is obtained from two excimer lasers, Lambda Physik
EMG 150 and Lambda Physik LPX 100, operated with
2
2
2
nm have been investigated in great detail.16h25 The large
decrease of the Ñuorescence lifetime upon deuteration19 and
the lack of Ñuorescence from vibrationally excited benzyl
radicals26 both indicate the occurrence of internal conversion
into the ground electronic state, which is of particular impor-
tance for this work. Transitions to higher electronically
excited states27h30 have been found between 305 and 229 nm.
The strongest absorption within this range is at the center of
the 12B È42B transition (see e.g., ref. 10) at 253 nm. To date,
ArÈF ÈHe and XeÈHClÈHe mixtures to produce laser light at
2
193 nm (11 ns, typically 3 mJ cm~2) and 308 nm (18 ns, typi-
cally 16 mJ cm~2), respectively. The laser Ñuences are either
measured directly with a calibrated GenTec ED-200 Joule-
meter or determined by actinometry (see ref. 33). A delay gen-
erator is used to set the delay time between the laser pulses.
The two excitation laser beams and the analysis light from a
continuous XeÈHg arc lamp (Ushio UXM-200H, 200 W) are
guided beam-in-beam (diameter 0.7 cm) through the cylin-
drical glass reaction cell (length 50 cm, diameter 2.3 cm). A
quartz prism double monochromator (Zeiss MM12) dispersed
the transmitted analysis light and its intensity was recorded by
a photomultiplier (RCA 1P28A) connected to an ampliÐer
(LeCroy LRS 133 B) and a transient digitizer (LeCroy TR
8837 F).
2
2
no experimental evidence of Ñuorescence from these excited
electronic states has been found and rapid internal conversion
to the ground electronic state is very likely to occur. Red-shift
and broadening of the bands in the UV absorption spectrum
with increasing temperature has been observed in shock wave
experiments.9,13
Vibrationally excited benzyl radicals in the ground elec-
tronic state are prepared through unimolecular decomposition
of ethylbenzene after UV excitation at 193 nm and subsequent
rapid internal conversion. Ethylbenzene has been employed as
the benzyl precursor for the following reasons:
(i) The dissociation of ethylbenzene after 193 nm excitation
into benzyl and methyl [k(52960 cm~1) \ 2 ] 107 s~1]10,14 is
much faster than the collisional deactivation under our experi-
mental conditions and therefore the quantum yield for benzyl
Usually, some hundred experiments were averaged to
obtain a satisfactory signal-to-noise ratio. Gas mixtures of the
ethylbenzene and the collider gas (argon) were prepared in a
100 l bulb. To avoid depletion of the ethylbenzene and also
accumulation of products the gas mixture continuously Ñowed
through the reaction cell. The gas pressure in the cell and the
Ñow velocity were adjusted by Hoke needle valves (1315G6Y/
mm, c \ 0.024) installed at the inlet and at the outlet of the
V
formation, U (P), is always close to unity. This ensures suffi-
reaction cell.
B
ciently large benzyl concentrations. U (P) can be extracted
Ethylbenzene (Aldrich, [99%) was carefully degassed by
pumpÈfreeze cycles before use but the bath gas (Ar, Messer
Griesheim, 99.998%) was applied without further puriÐcation.
B
from the measured dissociation rate in ref. 10 and the col-
lisional energy transfer data with argon from ref. 34.
82
Phys. Chem. Chem. Phys., 1999, 1, 81È90

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Determination of the yield of fragmentation
is too fast to be resolved. Therefore, the absorption step rep-
resents the fast formation of benzyl radicals. The subsequent
increase of the absorption is due to the strong increase of the
absorption cross section of the benzyl radical during its col-
lisional deactivation. The absorption reaches its maximum
value when the deactivation is complete. Slow benzyl loss due
to di†usion out of the observation volume and also due to
subsequent reactions accounts for the weak absorption
decrease at longer times.
ProÐle 2 in Fig. 2 corresponds to the formation of benzyl
from ethylbenzene after excitation at 193 nm and additional
excitation of benzyl at 308 nm after a delay time 250 ns. Both
excitations at 193 and 308 nm are not resolved and are to be
found within the absorption step. The interpretation of proÐle
2 is analogous to that of proÐle 1. However, the comparison
of the Ðnal absorption of both proÐles conÐrms that the addi-
tional excitation at 308 nm causes a deÐnite loss of benzyl
radicals.
The absolute yield of fragmentation of benzyl radicals Y (t )
due to the absorption of the 308 nm pulse is given by
d
c (P) [ c(P, t )
0
d
Y (P, t ) \
(5)
d
c (P)
0
where c (P) corresponds to the concentration of the initially
0
prepared benzyl radicals at a total pressure P and c(P, t ) is
d
given by the residual benzyl concentration after 308 nm exci-
tation at the delay time t .
d
Experimentally, all benzyl concentrations were determined
spectroscopically using UV-absorption (see e.g., refs 34 and
35) after complete collisional deactivatation. The analysis
wavelength of 252.4 nm is close to the maximum of the benzyl
absorption spectrum at 253 nm [see refs 10 and 36, e(252.4
nm, 300 K) \ 9.0 ] 10~17 cm2]. At this analysis wavelength
the contribution to the absorption from other species than
benzyl can safely be neglected. For a reliable determination of
fragmentation yields the following points were considered: (i)
All benzyl concentrations [c (P) and c(P, t )] have to be deter-
Both absorptionÈtime proÐles are taken at the analysis
wavelength of 252.4 nm. They arise from averaging over 150
single experiments. To guarantee identical experimental condi-
tions for the two di†erent absorptionÈtime proÐles they were
recorded by switching between single pulse excitation at 193
nm and double pulse excitation at 193 nm and delayed 308
nm excitation during the averaging procedure.
0
d
mined under identical experimental conditions. (ii) The highest
sensitivity for the UV absorption measurement is reached
after complete collisional deactivation of the benzyl radicals at
about 20 ls. Therefore, the concentration of the benzyl rad-
icals has to be kept sufficiently small so that radicalÈradical
reactions can be disregarded during this time interval. (iii) A
high excess of the bath gas Ar ensures that excited benzyl rad-
icals are predominately deactivated by collisions with Ar. The
resulting high total pressure (P4 mbar Ar) also prevents
benzyl radicals from rapidly di†using out of the observation
volume within the time interval of the experiment. (iv)
However, the total pressure must be below an upper limit
(O16 mbar Ar) to provide a high dissociation yield of the
benzyl precursor ethylbenzene and, thus, sufficiently large
benzyl concentrations. (v) The Ñuence of the excitation laser
must be sufficiently small (O16 mJ cm~2) to minimize multi-
photon excitation of the benzyl radicals.
At the analysis wavelength of 252.4 nm the absorption is
completely governed by the benzyl radicals and contributions
from any other species can conÐdently be neglected. We mea-
sured the absorption over the optical path length l, always
after complete vibrational relaxation of the benzyl radicals,
which is indicated by the dependence of the absorption cross
section e(t ) on the relaxation time t :
r
r
1
A
I (P)
I(P)
B
0
c (P) \
] ln
O
e(t )l
r
1
A
I (P)
B
0
c(P, t ) \
] ln
(6)
d
e(t )l
I(P, t )
r
d
I (P) is the light intensity initially transmitted through the
reaction cell while I(P) and I(P, t ) are the Ðnal transmitted
light intensities when the benzyl radicals are vibrationally
0
Results
Experimental fragmentation yields
d
relaxed. I(P) stands for the experiment where only benzyl rad-
icals are prepared after Ðring only the 193 nm laser (proÐle 1
In Fig. 2 absorptionÈtime proÐles obtained from a typical
experiment are shown. ProÐle 1 results from the single pulse
excitation of ethylbenzene at 193 nm. The formation of benzyl
radicals proceeds with a time constant of less than 50 ns10 and
in Fig. 2), and I(P, t ) stands for the experiment were the
0
delayed excitation laser at 308 nm (proÐle 2 in Fig. 2) has also
been Ðred. The absolute yield of fragmentation [as given by
eqn. (5)] can then be determined from the relative change of
the absorption. For weak absorptions this simpliÐes to
I (P) [ I(P, t )
0
d
Y (P, t ) \ 1 [
(7)
d
I (P) [ I(P)
0
It should be noted that the absorption cross section e(t ) and
r
the optical path length l both cancel, provided identical relax-
ation times are considered. However, as seen in Fig. 2 there is
some uncertainty in the determination of the residual light
intensities due to the minor loss of benzyl radicals at longer
lifetimes. The absolute values of the observations c (P) and
0
c(P, t ) may be a†ected in the worst case by as much as 10%
d
while the ratio c (P)/c(P, t ) is almost una†ected. One can
0
d
easily correct for most of the losses and estimate a relative
uncertainty in the experimentally determined dissociation
yields of about 5È10%.
The resulting benzyl dissociation yields are shown in Fig. 3.
The dissociation yield decreases with increasing delay times
between the two laser pulses and it also decreases with
increasing inert gas pressure. This observation is obviously
due to the lower internal excitation energy of the benzyl rad-
icals due to the increasing number of deactivating collisions
between the two laser pulses at longer delay times and higher
Fig. 2 AbsorptionÈtime proÐles at 252.4 nm from benzyl radicals
(see text): (1) after preparation through photodissociation of ethyl-
benzene at 193 nm (Ñuence: 3 mJ cm~2); (2) after preparation through
photodissociation of ethylbenzene at 193 nm (3 mJ cm~2) and a 250
ns delayed subsequent excitation at 308 nm (16 mJ cm~2).
[p(ethylbenzene): 0.030 mbar; p(argon): 4.0 mbar; T \ 298 K].
Phys. Chem. Chem. Phys., 1999, 1, 81È90
83

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Fig. 3 Variation of the benzyl dissociation yield with the delay time
Fig. 4 AbsorptionÈtime proÐles at 308 nm from benzyl radicals
during collisional deactivation after preparation from dissociation of
ethylbenzene at 193 nm (4 mJ cm~2). [p(ethylbenzene): 0.026 mbar;
p(argon): 4.0 mbar; T \ 298 K].
t between the two laser pulses at 193 nm (3 mJ cm~2) and 308 nm (16
d
mJ cm~2) [L: p(Ar) \ 4 mbar; =: p(Ar) \ 8 mbar, |: p(Ar) \ 16
mbar].
nometry we determined an absorption cross section of the ini-
inert gas pressure. Thus dissociation after 308 nm excitation
can more efficiently be suppressed by collisional deactivation.
tially formed benzyl radicals to be e(308 nm, t \ 0) \ (3.4
d
^ 0.1) ] 10~18 cm2. The subsequent change of absorption
with time is caused by the collisional deactivation of benzyl
radicals by the bath gas argon. The Ðnal absorption after
complete relaxation of the benzyl radicals is not shown. The
characteristic changes of the absorption result from the UV-
absorption band of benzyl, which is located near 305 nm at
300 K10 and which undergoes broadening and red-shift with
increasing temperature and thus increasing internal energy.
As we are mostly interested in the dependence of the frag-
mentation quantum yield U (P, t ) on the delay time t
between the two laser pulses we consider only the relative
fragmentation quantum yields. Thus only the relative changes
of the excitation absorption cross section with the delay time
and not their absolute values are considered.
Quantum yields
Initially ““coldÏÏ benzyl radicals show a quantum yield for
internal conversion after 308 nm excitation close to unity (see
the literature cited in ref. 15). The fragmentation (or
rearrangement) of benzyl radicals in the electronically excited
state prior to internal conversion is only of minor importance.
Decomposition or rearrangement in the electronically excited
state can only occur if it competes with internal conversion. In
general, internal conversion and the subsequent much slower
unimolecular decomposition on the ground state surface occur
on di†erent time scales and therefore are well separated.
Unimolecular decomposition on the ground state surface can
easily be quenched by collisions at low pressures (here ca. 4
mbar argon). Thus, decomposition in the electronically excited
state should lead to a non-quenchable contribution to the
quantum yield of decomposition. From Fig. 6 (see below) one
may estimate an upper limit for decomposition in the elec-
tronically excited state of less than 5% which is without sig-
niÐcance for this paper. As, generally, the quantum yield for
internal conversion increases with increasing internal energy
we assume a constant quantum yield of unity for all initial
internal excitation energies of the benzyl radicals that are rele-
vant in this study.
F
d
d
U (P, t )
e(308 nm, t \ 0)
Y (P, t )
F
d
d
d
\
]
(9)
U (P, t \ 0)
e(308 nm, t )
Y (P, t \ 0)
F
d
d
d
For a comparison of absolute quantum yields at di†erent total
pressures the pressure dependence of the fragmentation
quantum U (P, t \ 0) must be known. As the quantum yield
F
d
for benzyl fragmentation approaches unity under collision free
conditions [U (P \ 0) \ 1] we approximate U (P \ 0, t \ 0)
B
F
d
by U (P \ 4 mbar, t \ 0), and Y (P \ 0, t \ 0) by Y (P \ 4
F
d
d
mbar, t \ 0). The required quantum yield for dissociation of
benzyl radicals U (P, t ) can be approached by
d
Then the quantum yield for fragmentation U (P, t ) of the
benzyl radicals can be expressed in terms of the fragmentation
F
d
F
d
e(308 nm, t \ 0)
d
U (P, t ) \
yield Y (P, t ) of eqn. (5), the Ñuence of the excitation laser
F
d
d
e(308 nm, t )
F (308 nm), and the absorption cross section of benzyl radicals
d
l
Y (P, t )
at the excitation wavelength e(308 nm, t ), which depends on
d
]
(10)
d
the delay time t between the 193 nm photolysis and the 308
d
Y (P \ 4 mbar, t \ 0)
d
nm excitation laser. At a given total pressure the delay time
Multiphoton contribution
determines the number of deactivating collisions before reexci-
tation and hence the vibrational excitation energy of the
benzyl radicals. For weak absorptions the expression sim-
pliÐes to
Under our experimental conditions the quantum yield for dis-
sociation after absorption of two or more photons at 308 nm
is always close to unity and almost independent on the bath
gas pressure and on the delay time between the two laser
pulses. We investigated the multiphoton contribution to the
fragmentation yield by varying the Ñuence of the 308 nm exci-
tation laser pulse. The results are presented in Table 1 and
visualized in Fig. 5. With no delay time between the two laser
pulses and at a total pressure of 4 mbar Ar [curve (a) in Fig.
5] the dissociation quantum yield is always unity within the
limits of the experiments. Under these conditions benzyl rad-
icals always decompose when they have absorbed at least one
photon at 308 nm. However, at longer delay times, and there-
fore with increasing number of deactivating collisions before
excitation, most of the benzyl radicals which have absorbed
Y (P, t )
d
U (P, t ) \
(8)
F
d
e(308 nm, t ) ] F (308 nm)
d
l
For a conversion of the fragmentation yields into dissociation
quantum yields these excitation cross sections of vibrationally
highly benzyl radicals have to be known. Therefore, we mea-
sured the absorptionÈtime proÐle at 308 nm during the col-
lisional deactivation of benzyl radicals after formation from
unimolecular decomposition of ethylbenzene after excitation
at 193 nm. The result is presented in Fig. 4. As in Fig. 2 the
absorption step is due to the formation of vibrationally
excited benzyl radicals in the ground electronic state. By acti-
84
Phys. Chem. Chem. Phys., 1999, 1, 81È90

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Table 1 Quantum yield for fragmentation of benzyl radicals after
excitation with 308 nm for Z [M]t \ 0 and 90 collisions between
LJ
d
the laser pulses. [p(Ar) \ 4 mbar]
Fluence
mJ cm~2
U (P, Z Pt \ 0)
U (P, Z Pt \ 90)
F
LJ
d
F
LJ d
16
28
62
1.09
0.94
0.97
0.15
0.23
0.32
only one photon will be collisionally stabilized. However, that
fraction of radicals which has absorbed two and more 308 nm
photons will always decompose. Thus curve (b) in Fig. 5
shows the increasing contribution of multiphoton processes to
the fragmentation quantum yield with increasing Ñuence. The
delay time between the two laser pulses corresponds to about
90 Lennard-Jones collisions (again at a total pressure of 4
mbar Ar). The quantum yields for fragmentation after single
Fig. 6 Quantum yields for benzyl fragmentation U as a function of
F
the number of Lennard-Jones collisions (Z [Ar]t ) with argon
LJ
d
between the two laser pulses at 193 and 308 nm at T \ 298 K.
Experiments: (…) p \ 4 mbar; (+) p \ 8 mbar; (=) p \ 16 mbar.
photon excitation of U \ 0.1 is given by the intercept for
F
Ñuence ]0. At a Ñuence of 16 mJ cm~2 we Ðnd a quantum
Model calculations: ()) and upper dashed line, s \ 16.83; (L) and
eff
yield U \ 0.15, indicating a multiphoton contribution of 0.05.
full line, s \ 17.33; (È) and lower dashed line, s \ 17.83, all other
F
eff
eff
As the Ñuence of the excitation laser was kept at 16 mJ cm~2
parameters identical [for k(E): E \ 29 240 cm~1, A \ 5 ] 1013 s~1,
0
for energy transfer: C \ 43.5 cm~1, C \ 4.2 ] 10~3, y \ 0.55]
there is only a minor contribution of multiphoton excitation
to the total dissociation yield. Accordingly, we corrected our
experimental quantum yields. The dependence of the corrected
quantum yield for benzyl decomposition on the number of
deactivating collisions between the two laser pulses is present-
ed in Fig. 6. Again we estimate a relative uncertainty of about
5È10% for the individual experimental points.
0
1
to the formation of bibenzyl (C
reaction
H
) in the radical self-
14 14
C H ~ ] C H ~ ] M ] C
H
] M
(11)
7
7
7
7
14 14
and the reformation of ethylbenzene (C H ) through the
recombination with methyl radicals, the second product from
the ethylbenzene dissociation,
8
10
Benzyl loss by di†usion and by recombination
Under identical experimental conditions of pressure and tem-
perature the loss-rate of benzyl due to di†usion out of the
observation volume depends only on the concentration gra-
dient perpendicular to the direction of observation. As the 193
nm laser pulse always prepares identical benzyl concentrations
the concentration gradients, and therefore the di†usion losses,
are also identical. However, when the 308 nm excitation laser
is Ðred, at most 10% of the initially prepared benzyl radicals
are decomposed (Fig. 3). Therefore, the benzyl radical concen-
tration gradient is almost unchanged and the resulting error
in the fragmentation yield [see eqn. (5)] due to benzyl radical
di†usion is estimated to be less than 1% and hence well below
the total uncertainty of the experiment.
C H ~ ] CH ~ ] M ] C H ] M
(12)
7
7
3
8 10
can easily be estimated from the initial radical concentrations
c (P), the reaction time (t ), and the recombination rate con-
0
r
stants from the literature. Reaction (12) has almost no e†ect
because most of the methyl radicals recombine in the fast self-
reaction
~CH ~ ] ~CH ] M ] C H ] M
(13)
3
3
2 6
Under typical experimental conditions we have an initial
benzyl concentration of c (P) B 5 ] 10~11 mol cm~3, identi-
0
cal to the initial methyl radical concentration. During a
typical deactivation time of t B 20 ls we estimate with k
B
However, more important non-dissociative loss of benzyl
radicals originates from benzyl radical recombination
reactions11,37 during the time interval of about 20 ls needed
for complete relaxation (Fig. 2). The relative loss of benzyl due
r
11
2.3 ] 1012 cm3 mol~1 s~1,11 k B 8.2 ] 1012 cm3 mol~1
12
s~1,10 and k B 3.6 ] 1013 cm3 mol~1 s~1,38 a total addi-
13
tional loss of benzyl radicals of less than 2%. As only about
10% of the benzyl radicals are dissociated by the excitation
laser the initial concentrations of benzyl and methyl are
almost identical whether the 308 nm excitation laser has been
Ðred or not. Consequently, the dissociation yields of benzyl
Y (t ) determined by eqn. (5) are almost une†ected by reactions
d
(11)È(13) because these benzyl losses almost completely cancel.
However, when benzyl radicals have been dissociated from
308 nm excitation there is a further loss reaction. According to
reaction (1) hydrogen atoms are formed which, in a very fast
reaction with benzyl radicals,11 produce toluene (C H )
7
8
C H ~ ] H~ ] M ] C H ] M
(14)
7
7
7 8
This reaction causes an additional loss of benzyl radicals
during the benzyl relaxation time which does not cancel in
eqn. (5). As the observed total relative change of the benzyl
concentration is usually less than 10% we can estimate the
maximum systematic error in the dissociation yield Y (P, t )
introduced by reaction (14). The total amount of hydrogen
atoms initially formed corresponds at maximum to the
observed benzyl loss after excitation at 308 nm. Under typical
d
Fig. 5 Fluence dependence of the quantum yield for benzyl fragmen-
tation U at 308 nm. (…) Benzyl radicals excited directly after prep-
F
aration (Z [M]t \ 0); (=) benzyl radicals excited after 90
LJ
d
Lennard-Jones collisions (Z [M]t \ 90) [p(ethylbenzene): 0.026
LJ
d
mbar; p(argon): 4.0 mbar; T \ 298 K]
conditions we have an initial benzyl concentration of c (P) B
0
Phys. Chem. Chem. Phys., 1999, 1, 81È90
85

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5 ] 10~11 mol cm~3 and at maximum a total dissociation
yield Y (P, t ) of about 10%. Therefore, the initial concentra-
d
tion of hydrogen atoms is below 5 ] 10~12 mol cm~3. During
typical deactivation times of t B 20 ls and with a rate con-
r
stant of k \ 2.0 ] 1014 cm3 mol~1 s~1,39 the total loss of
14
hydrogen atoms is ca. 20%. Therefore, an initial benzyl disso-
ciation yield of Y (P, t \ 0) + 0.10 will increase to a value of
d
0.12 due to subsequent loss of benzyl radicals from reaction
(14). However, this is clearly an overestimate because any
other loss of hydrogen atoms as their fast di†usion out of the
observation volume and as reactions with other constituents
such as ethylbenzene, methyl radicals, etc. will reduce the
inÑuence of reaction (14). Although this is a systematic error,
we have not corrected our experimentally determined frag-
mentation yields as the inÑuence decreases with decreasing
dissociation yield and the experimental uncertainty for the
individual experimental points is larger or of the same order
of magnitude.
Fig. 7 Temporal evolution of the population distribution of benzyl
radicals in collisions with argon. (a) Initial distribution from the disso-
ciation of ethylbenzene; (b), (c), (d) and (e) after 25, 50, 75, and 100
Lennard-Jones collisions (Z [Ar]t ), respectively.
Modeling the fragmentation quantum yields of benzyl radicals
LJ
d
It is the goal of the modeling to determine the rate constant
k(E) of benzyl fragmentation. The model calculations are
carried out in the following way: (1) Calculation of the initial
population distribution of benzyl radicals produced from the
dissociation of the vibrationally excited ethylbenzene precur-
sor. (2) Computation of the temporal evolution of the popu-
lation distribution during the collisional deactivation of
benzyl radicals before the excitation pulse at 308 nm. (3)
Determination of the population distribution of benzyl rad-
icals after absorption of the excitation laser pulse at 308 nm.
(4) Calculation of the fragmentation quantum yield resulting
from competition between dissociation rates [k(E)] and col-
lisional deactivation rates. (5) Variation of k(E) until the
Therefore, the fragmentation quantum yield U (t ) does not
only depend on the average energy of the benzyl radicals but
F d
also to some extent on the shape of their distribution function
(see below).
It should be noted that some ethylbenzene molecules have
lost some energy in collisions with the bath gas molecules
before their dissociation. However, the decrease of the
quantum yield for benzyl radical formation U (P) with
B
increasing the inert gas pressure is known10 and has been
taken into account.
In addition, the average excitation energy of the initially
prepared benzyl radicals is somewhat smaller compared with
benzyl radicals obtained from the collision free dissociation of
ethylbenzene. The rates for collisional deactivation of hydro-
carbons and for collisional deactivation of radicals of similar
size are almost identical.15,43,54 As only a small amount of
energy is removed from ethylbenzene before dissociation it
can safely be assumed that the width of the initial population
distribution of the benzyl radicals is not altered. However, the
entire distribution function is shifted to lower energies that
correspond to the average energy loss of the ethylbenzene
molecules. Therefore, we proceed with the assumption that
ethylbenzene molecules dissociate immediately after their exci-
dependence of the fragmentation quantum yields U on the
F
number of Lennard-Jones collisions (Z [M]t ) between
the two laser pulses is reproduced.
LJ
d
Initial population distribution of the benzyl radicals. The
vibrational energy distribution of benzyl radicals prepared by
dissociation of the ethylbenzene precursor has been calculated
using the phase space limit of statistical unimolecular rate
theory. The procedure is straightforward and has been exten-
sively described in the literature52,53 and also in our paper on
energy transfer.15 As the total energy for the decomposition of
an almost microcanonical ensemble of vibrationally excited
ethylbenzene is well known, the energy partitioning in the dis-
sociation essentially depends on the CwC bond energy, on
the moments of inertia, and on the densities of states of the
two fragments, i.e. the benzyl and methyl radicals.
The resulting population distribution is quite broad and is
shown in Fig. 7 as curve (a). The location of the energy dis-
tribution essentially depends on the CwC bond energy in eth-
ylbenzene which has been calculated from the standard
enthalpies of formation of ethylbenzene,40 the benzyl,41 and
the methyl radical.42 The average initial vibrational energy of
the benzyl radicals is calculated to be SET \ 20 560 cm~1 and
we estimate an uncertainty of less than 1000 cm~1. The width
of the energy distribution of about 6000 cm~1 (FWHM) is
mostly determined by the phase space volumes of the two
fragments. Therefore, the uncertainty in the width is approx-
imately given by the relative uncertainties in the vibrational
densities of states of the benzyl and the methyl radical. We
estimate an uncertainty of the width of less than 10%.
tation with a quantum yield (U ) of eqn. (3). Benzyl radicals
B
are prepared with an initial population distribution that cor-
responds to collision free dissociation; however, this distribu-
tion is shifted to lower energies according to the energy loss in
ethylbenzene. Subsequently, this population distribution is
then collisionally deactivated.
Collisional deactivation of benzyl radicals. As the total rate
for collisional deactivation of benzyl radicals with Ar has been
studied in ref. 15 we are able to quantitatively characterize the
population distribution function of benzyl radicals during
their collisional deactivation before the laser excitation pulse
at 308 nm.
For this purpose we describe the collisional energy transfer
in terms of a master equation where the bimolecular rate con-
stants for the collisional energy transfer are given by the
product of the Lennard-Jones collision frequencies Z and
LJ
the collisional energy transfer probability function P(E@, E).
For excitation energies (E) greater than the threshold energy
As a consequence, further excitation at 308 nm will create
highly vibrationally excited benzyl radicals with a population
distribution of the initial width and a speciÐc rate constant for
fragmentation that varies within the energy range of the popu-
lation distribution. The collisional deactivation may lead to
some additional broadening of the population distribution.
E , the competition between the unimolecular decomposition
and the speciÐc rate constant k(E) has been included. We
assume that rotational energy transfer is fast compared with
vibrational energy transfer and therefore the rotational energy
distribution of vibrationally excited benzyl radicals can always
be approximated by a thermal rotational distribution at 300
0
86
Phys. Chem. Chem. Phys., 1999, 1, 81È90

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K. The resulting system of di†erential equations has been
solved by calculation of the eigenvalues and the eigenvectors
as described in refs 44 and 45.
Based on a knowledge of similar collisional energy transfer
rates for benzyl radicals15 and toluene molecules34,46 we
adopted the collisional energy transfer probability function as
derived for the deactivation of vibrationally excited toluene
molecules in collisions with Ar from ref. 47
Calculation of quantum yields for fragmentation. As we have
characterized the initial population distribution of the benzyl
radicals after absorption of the excitation laser we calculate
the dissociation yield from the solution of the same master
equation for the new initial conditions. The quantum yield for
fragmentation U (P, t ) is provided by the ratio of initial and
Ðnal concentration of benzyl radicals. Because we normalize
all concentrations to the initial concentration of the excited
benzyl radicals it is sufficient to calculate the Ðnal population
distribution function [eqn. (18)]
F
d
1
G A E [ E@ BH
y
P(E@, E) \
exp
[
N(E)
C ] C E
0
1
P=
] o(E)o(E@)dE dE@
(15)
U (P, t ) \ 1 [
g*(E*, t ] O) dE*
(18)
F
d
0
The energies before and after the collision are denoted by E
and E@, respectively, and o(E) and o(E@) represent the corre-
sponding vibrational densities of states. Thus o(E)dE and
o(E@)dE@ correspond to the degeneracy of the initial and of the
Ðnal energy bin, respectively. N(E) stands for the normal-
ization constant and the parameters C \ 43.5 cm~1, C \ 4.2
As described in refs 44 and 45 we solved the master equation
by calculating both the eigenvalues and the eigenvectors. Thus
an analytical expression for the temporal evolution of the
population distribution is provided. The Ðnal fraction of sta-
bilized benzyl radicals is given by summing the components of
0
1
the eigenvector belonging to the highest eigenvalue (j \ 0).
] 10~3, and y \ 0.55 describe the shape of the collisional
energy transfer probability for deactivating collisions with
argon (E [ E@). The probability for activating collisions
(E@ [ E) is given from the principle of detailed balancing:
k
SpeciÐc and thermal high pressure rate constants
In general, the thermal high pressure limiting rate constant for
a unimolecular dissociation reaction k (T ) is given by the
o(E@) G AE@ [ EBH
=
P(E@, E) \ P(E, E@)
exp [
(16)
thermal average of the microcanonic rate constants k(E, J),
o(E)
k T
which depend on the internal energy E and also on the total
angular momentum J of the dissociating molecule [eqn. (19)]
B
We calculated the vibrational density of states using the fre-
quencies of the benzyl radical as given in ref. 5. Within the
relevant range of energies there is no di†erence between
the results from the BeyerÈSwinehart algorithm48 and the
WhittenÈRabinovitch approximation.49
P= P=
k (T ) \
k(E, J) ] f (E, J) dE dJ
(19)
=
0
E0
E
denotes the threshold energy and f (E, J) the energy and
0
As we introduced the degeneracies into the collisional
energy transfer probability function in eqn. (15) we had to
alter the parameter y from the initial value of 0.7 in ref. 47 to
0.55 to reproduce an identical time development in the relax-
ing population distribution. More details are described in ref.
44 and in a forthcoming paper.45 In Fig. 7 the resulting popu-
lation distributions of benzyl radicals after 0, 25, 50, 75, and
100 deactivating collisions are shown.
angular momentum probability distribution at thermal equi-
librium. This probability distribution is given by the Boltz-
mann distribution and can be calculated from the vibrational
density of states o(E, J) and the partition function Q
A
E
B
o(E, J)exp [
k T
B
f (E, J) \
(20)
Q
Population distribution of benzyl radicals before dissociation.
The 308 nm laser excites the benzyl radicals after the delay
Within the formulation of the statistical adiabatic channel
model (SACM) the microcanonical rate constant k(E, J) can
be expressed as
time t . The resulting population distribution g*(E*) is
d
entirely determined by the initial population distribution g(E,
t ), the absorption cross section e(E), the energy of the
W (E, J)
ho(E, J)
d
k(E, J) \
(21)
absorbed photon (hl), and the laser Ñuence F (308 nm):
l
g*(E*) \ g(E, t ) ] e(E) ] F (308 nm)
(17)
where h is PlanckÏs constant and W (E, J) denotes the number
of open channels for dissociation at a given energy E and total
angular momentum J. Thus the thermal unimolecular rate
constant
d
l
The excitation energy E* is simply given by E* \ E ] hl.
With a maximum average energy of SET \ 20 560 cm~1 at no
delay between the two laser pulses (t \ 0) the Ðnal maximum
d
average energy of the benzyl radicals is SE*T \ 53 030 cm~1.
k T
h
Qj
Q
A
E
B
For evaluation of the population distribution the energy
dependence of the absorption cross section has to be taken
into account. For this purpose, in general, absorption cross
sections of excited benzyl radicals for microcanonical energy
distributions with di†erent excitation energies E are required.
However, it has been shown that for vibrationally excited
azulene,50 and also for vibrationally excited toluene,51 the
absorption cross sections for microcanonical and canonical
energy distributions are almost identical for similar average
excitation energies SET of the two distributions. We assume a
similar behaviour for vibrationally excited benzyl radicals so
that the dependence of the absorption cross section on the
excitation energy e(E) can be replaced by the dependence on
the average excitation energy e(SET) and thus by the depen-
dence on the number of deactivating collisions e(Z [M]t ), as
B
0
k (T ) \
]
] exp [
(22)
=
k T
B
is determined by the integral over the Boltzmann weighted
number of open channels:
P
=
P
=
A
E [ E B AE [ E
B
0
0
Qj \
W (E [ E ) ] exp [
d
dJ
0
k T
k T
0
0
B
B
(23)
Hence the Arrhenius expression from eqn. (2) can be used to
deÐne the pseudo-partition-function Qj as
h
A
E [ E
k T
B
a
0
Qj \ QA
exp [
(24)
k T
LJ
d
B
B
shown in Fig. 4. It is important to note, that the total number
of excited radicals increases with increasing delay time
between the two laser pulses because of the increase of the
absorption cross section.
where A and E represent the pre-exponential factor and the
activation energy, respectively. Unfortunately, the threshold
a
energy E for reaction (1) is not accurately known. However,
0
Phys. Chem. Chem. Phys., 1999, 1, 81È90
87

View Article Online
in the high pressure limit the di†erence between the activation
eqn. (2). The parameters A and s can be Ðtted to express the
eff
energy E and the threshold energy E is generally small so
speciÐc rate constant within a limited range of energy.55 The
a
0
that in a Ðrst approximation it may be set to zero. The
resulting uncertainty is unimportant in particular as we also
have to neglect the J-dependence of the speciÐc rate constant
for the dissociation of benzyl radicals. This is a consequence of
the unknown mechanism of the benzyl fragmentation in which
the rigidity of the transition state is still unclear. With these
simpliÐcations we will perform an inverse Laplace transform-
ation of this pseudo-partition-function Qj, which will then
parameter A is a scaling parameter and s characterizes the
eff
steepness of the k(E)-curve.
The simulation is started with k(E) which is represented by
the parameters A \ 1 ] 1014 s~1, s \ 17.83, and E \
eff
0
29 240 cm~1 as obtained by Ðtting expression (26) to the k(E)
values obtained from the deconvolution of the thermal high
pressure rate constant [see curve (a) in Fig. 8]. Then the
parameters A and s are varied until the experimentally
eff
give a deconvoluted number of open channels W (E) that is
determined quantum yields for fragmentation U (P, t ) are
vib
F
d
somewhat averaged over the angular momentum distribution.
reproduced by the simulation. The result is shown as the full
Thus the rotationally averaged speciÐc rate constant k (E) is
given by
line in Fig. 6. Obviously, the three parameters, A, s , and E ,
cannot be determined independently from this procedure.
vib
eff
0
Various sets of (A, s , E ) lead to the same absolute value of
eff
0
W
ho (E)
(E)
k(E) and therefore reproduce the quantum yields for fragmen-
tation U (P, t ). However, the absolute k(E) values are more
vib
k
(E) \
vib
(25)
vib
F
d
reliable.
(see e.g. refs 52 and 53).
The result of the deconvolution procedure is shown as
curve (a) in Fig. 8. As the Arrhenius parameters A and E have
been obtained by Ðtting experimental data at temperatures
between 1500 and 1800 K, it should be pointed out that
within the experimental uncertainty the thermal high pressure
The sensitivity of the calculated quantum yields to the spe-
ciÐc rate constants is demonstrated in Fig. 6. A variation of
a
the speciÐc rate constant by a factor of two causes at U (P,
F
td) \ 0.5 a shift of the simulated curve by about ten collisions,
corresponding to a change of the excitation energy of about
1200 cm~1. The parameters A and s have both been varied.
rate constants can be reproduced by various pairs of (A, E )-
eff
a
values. Therefore, we estimate the precision of E to be within
a
If A varies by a factor of two the same change in the quantum
yield is reached as when s is altered by ^0.5. The delay time
about 7%. The speciÐc rate constants obtained are most reli-
eff
dependency of the quantum yield is best simulated with the
able for vibrational energies around 50 000 cm~1, which cor-
respond to excitation energies of thermally dissociating benzyl
radicals between 1500 and 1800 K. In addition, this thermal
excitation energy is very similar to the vibrational energy of
the benzyl radicals prepared by the laser excitation procedure
presented in this paper. Typically one has to accept that the
following parameters of eqn. (26): A \ 5.0 ] 1013 s~1, s
\
eff
17.33, and E \ 29 240 cm~1 (full line in Fig. 6). The sensi-
0
tivity of the quantum yields to the parameter s is also shown
eff
in Fig. 6 where the upper and lower dashed lines (d and c) are
the results of additional simulations with s \ 16.83 and
eff
s
\ 17.83, respectively.
k
(E)-values will be uncertain within a factor of 2 to 3. This
eff
vib
The inÑuence of the width of the population on the
has been shown in the case of the isomerization of azulene by
comparing deconvoluted and directly measured speciÐc rate
constants.54
quantum yield can be estimated from the e†ective decomposi-
tion rate constant k of the benzyl radicals. For a normalized
eff
population distribution g(E), k can be calculated from the
eff
speciÐc rate constant as
Dependence on the speciÐc rate constant
P=
Following unimolecular rate theory, we represent the speciÐc
rate constant k(E) which enters the master equation by the
following analytical expression (Fig. 8)
k
\
k(E)g(E) dE
(27)
eff
0
After 308 nm excitation and internal conversion the average
energy of the benzyl radicals is ca. 50 000 cm~1 while the
energy distribution has a width (FWHM) of about 6000 cm~1.
A
E [ E
B
seff~1
0
k(E) \ A
(26)
E
Obviously, for a narrow distribution k approaches k(E).
According to our parameters we have at E \ 50 000 cm~1 a
E
denotes the threshold energy, which we identify with the
eff
0
activation energy of the high pressure limiting rate constant in
speciÐc rate constant of k(E) \ 1.20 ] 107 s~1. For Gaussian
populations with identical average energies SET at 50 000
cm~1 but di†erent widths (FWHM) of 2000, 4000, 6000, and
8000 cm~1, the calculated e†ective rate constant is 1.26, 1.46,
1.81, and 2.37 ] 107 s~1, respectively. Thus a population with
a width of 6000 cm~1 shows only a 50% higher e†ective rate
constant. Near 50 000 cm~1 the energy dependence of the spe-
ciÐc rate constant k(E) is given by d[ln k(E)]/dE \ 48%/1000
cm~1 while for a 6000 cm~1 wide distribution an almost iden-
tical energy dependence of d(ln k )/dE \ 46%/1000 cm~1 is
obtained. During collisional deactivation with an inefficient
eff
collider such as argon the average excitation energy of the
benzyl radicals decreases while the width of the distribution
remains almost unchanged (Fig. 7). We infer, that for our
experiments that the deconvolution process of the decomposi-
tion quantum yield is unique and reliable. The reason is given
by the relatively moderate increase of the speciÐc rate con-
stant of only about 50% per 1000 cm~1 within the width of
the energy distribution.
We conclude that the speciÐc rate constants can be deter-
mined with an accuracy of better than a factor of two within
the experimental accuracy. The extracted energy dependence
of the speciÐc rate constant is consistent with the predicted
Fig. 8 SpeciÐc rate constants k(E) for the unimolecular decomposi-
tion of benzyl radicals with a threshold energy of E \ 29 240 cm~1;
0
(a) from deconvolution of the thermal rate constant (A \ 1 ] 1014
s~1,
s
\ 17.83); (b) from the fragmentation quantum yield
eff
(A \ 5 ] 1013 s~1, s \ 17.33); (c) (A \ 5 ] 1013 s~1, s \ 17.83);
eff
eff
(d) (A \ 5 ] 1013 s~1, s \ 16.83).
eff
88
Phys. Chem. Chem. Phys., 1999, 1, 81È90

View Article Online
energy dependence of k(E) shown in Fig. 8. For comparison
these speciÐc rate constants are shown as curve (b) in Fig. 8.
The changes in the speciÐc rate constant by altering the
transfer.15 The subsequent unimolecular decomposition
should then be measured directly in a time resolved way by
either monitoring the formation of hydrogen atoms or the loss
of benzyl radicals. Then, the thermal decomposition rate con-
stant can be calculated by averaging the experimentally deter-
mined speciÐc rate constants over a wide range of internal
energies.
parameter s by ^0.5 to s \ 17.83 [curve (c)] and to s
\
eff
eff
eff
16.83 [curve (d)] are also displayed. The rate constants of the
two di†erent deconvolution methods disagree by about a
factor of three.
Acknowledgements
Dependence on the energy transfer parameter
The authors thank J. Troe and K. Luther for helpful dis-
cussions. Financial support of this work by the Deutsche For-
schungsgemeinschaft (SFB 357 ““Molekulare Mechanismen
unimolekularer Prozesse) is gratefully acknowledged.
We investigated the sensitivity of the fragmentation quantum
yields on the energy transfer parameters, C \ 43.5 cm~1,
0
C \ 4.2 ] 10~3, and y \ 0.55 from eqn. (15). We varied these
1
parameters in such a way that the average amounts of energy
transferred per collision S*ET did not vary more than 10%,
which corresponds to the uncertainty of the energy transfer
experiments from ref. 54. For identical k(E) curves the calcu-
lated quantum yields are almost insensitive to this variation of
the energy transfer parameters.
References
1
2
3
M. Szwarc, J. Chem. Phys., 1948, 16, 128.
R. D. Smith, J. Phys. Chem., 1979, 83, 1553.
V. S. Rao and G. B. Skinner, 21st International Symposium on
Combustion. The Combustion Institute, Pittsburgh, 1986, p. 809.
K. M. Pamidimukkala, R. D. Kern, M. R. Patel, H. C. Wei and
J. H. Kiefer, 21st International Symposium on Combustion, The
Combustion Institute, Pittsburgh, 1986, p. 585.
4
Discussion of the fragmentation
5
6
L. D. Brouwer, W. Muller-Markgraf and J. Troe, J. Phys. Chem.,
Within the internal energy range 47 000È50 000 cm~1 the spe-
ciÐc rate constants obtained from the simulation quantum
yields are smaller by a factor of about three compared with
the results from the inversion of the thermal high pressure rate
1988, 92, 4905.
M. Braun-Unkho†, P. Frank and Th. Just, 22nd International
Symposium on Combustion, The Combustion Institute, Pittsburgh,
1988, p. 1053.
H. Hippler, C. Reihs and J. Troe, Z. Phys. Chem., 1990, 167, 1.
M. B. Colket and D. J. Seery, 25th International Symposium on
Combustion, The Combustion Institute, Pittsburgh, 1994, p. 883.
W. Muller-Markgraf and J. Troe, J. Phys. Chem., 1988, 92, 4914;
W. Muller-Markgraf, PhD Thesis, University of Gottingen, 1987.
constant.
For
example,
one
obtains
k(50 000
7
8
cm~1) \ 3.8 ] 107 s~1 from the inverted thermal high pres-
sure rate constant and k(50 000 cm~1) \ 1.2 ] 107 s~1 from
the fragmentation quantum yields. The di†erence between the
two speciÐc rate constants is somewhat larger than the largest
possible di†erence calculated from the estimated errors of
each rate constant. Up to now the origin for this discrepancy
is not clear and in the following we discuss some possible
explanations.
The dependence of the speciÐc rate constant on angular
momentum has not been taken into account, neither for the
deconvolution of the thermal high pressure rate constant nor
for the simulation of the experiments described here. While
under thermal conditions the rotational distribution of benzyl
is given by the Boltzmann distribution for temperatures
around 1500 K, in the present experiments it is given by the
Boltzmann distribution for temperatures around 300 K.
However, for the dissociation of toluene it has been found that
the speciÐc rate coefficients do not di†er markedly for typical
values of the quantum number J at 1500 and at 300 K.10 The
situation for the benzyl fragmentation could be similar, espe-
cially if the reaction occurred via an isomerization as pro-
posed in ref. 11. Therefore, it seems to be unlikely that the
observed discrepancies between the speciÐc rate coefficients
from both experiments are only due to the di†erent rotational
distributions at the chosen experimental conditions.
The discrepancy between the speciÐc rate constants
obtained from both experiments may also be explained by the
mechanism of benzyl fragmentation. In deconvoluting the
thermal rate constant we assumed that the reaction occurs via
a simple one-step mechanism or that only one step of a more
complex mechanism is rate determining for all excitation ener-
gies. If the fragmentation of benzyl occurs via a more complex
mechanism, e.g. as proposed in ref. 11, where the rate con-
stants of several steps have to be taken into account the result
of the deconvolution might by physically meaningless and
should not be compared with the speciÐc rate coefficients
derived here.
We will test these hypothesis in further investigations where
we will directly determine speciÐc rate coefficients for the
unimolecular decomposition of benzyl radicals over a wide
range of internal energies. This can be done by exciting com-
pletely relaxed benzyl radicals with a single photon of appro-
priate energy in analogy to the experiments on energy
9
10 U. Brand, H. Hippler, L. Lindemann and J. Troe, J. Phys. Chem.,
1990, 94, 6305; L. Lindemann, PhD Thesis, University of Got-
tingen, 1987.
Ž
11 M. Braun-Unkhofff, P. Frank and Th. Just, Ber. Bunsen-Ges.
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