Kinetics of the self reaction of cyclohexyl radicals

Article abstract of DOI:10.1021/jp204012w

The kinetics of the self-reaction of cyclohexyl radicals was studied by laser photolysis/photoionization mass spectroscopy. Overall rate constants were obtained in direct real-time experiments in the temperature region 303 - 520 K and at bath gas (helium with up to 5% of radical precursors) densities (3.00-12.0)×10¹⁶ molecules cm^r3. Cyclohexyl radicals were produced by a combination of the 193 nm photolysis of oxalyl chloride ((CClO)₂) with the subsequent fast reaction of Cl atoms with cyclohexane, and their initial concentrations were determined from real-time profiles of HCl. The observed overall c-C₆H₁₁ + c-C ₆H₁₁ rate constants demonstrate negative temperature dependence, which can be described by the following expressions: k₁ = 4.8×10¹² exp(+542 K/T) cm³ molecule^-1 s^-1, with estimated uncertainty of 16% over the 303-520 K temperature range. The fraction of disproportionation equal to 41 ± 7% was determined at 305 K; analysis of earlier experimental determinations of the disproportionation-to-recombination branching ratio leads to recommending this room-temperature value for other temperatures. The corresponding temperature dependences of the recombination (1a, bicyclohexyl product) and the disproportionation (1b, cyclohexene and cyclohexane products) channels are k(1a) = 2.8×10^-12 exp(+542 K/T) and k(1b) = 2.0×10 ^-12 exp(+542 K/T) cm³ molecule^-1 s ^-1, with estimated uncertainties of 20% and 29%, respectively.

Full text of DOI:10.1021/jp204012w

ARTICLE
pubs.acs.org/JPCA
Kinetics of the Self Reaction of Cyclohexyl Radicals
Ksenia A. Loginova and Vadim D. Knyazev*
Research Center for Chemical Kinetics, Department of Chemistry, The Catholic University of America, Washington, DC 20064, United States
S Supporting Information
b
ABSTRACT: The kinetics of the self-reaction of cyclohexyl radicals was studied
by laser photolysis/photoionization mass spectroscopy. Overall rate constants
were obtained in direct real-time experiments in the temperature region 303 ꢀ
520 K and at bath gas (helium with up to 5% of radical precursors) densities
(3.00ꢀ12.0) ꢁ 1016 molecules cmꢀ3. Cyclohexyl radicals were produced by a
combination of the 193 nm photolysis of oxalyl chloride ((CClO)2) with the
subsequent fast reaction of Cl atoms with cyclohexane, and their initial
concentrations were determined from real-time profiles of HCl. The observed
overall c-C6H11 + c-C6H11 rate constants demonstrate negative temperature
dependence, which can be described by the following expressions: k1 = 4.8 ꢁ
10ꢀ12 exp(+542 K/T) cm3 moleculeꢀ1 sꢀ1, with estimated uncertainty of 16%
over the 303ꢀ520 K temperature range. The fraction of disproportionation
equal to 41 ( 7% was determined at 305 K; analysis of earlier experimental
determinations of the disproportionation-to-recombination branching ratio leads to recommending this room-temperature value
for other temperatures. The corresponding temperature dependences of the recombination (1a, bicyclohexyl product) and the
disproportionation (1b, cyclohexene and cyclohexane products) channels are k(1a) = 2.8 ꢁ 10ꢀ12 exp(+542 K/T) and k(1b) = 2.0
ꢁ 10ꢀ12 exp(+542 K/T) cm3 moleculeꢀ1 sꢀ1, with estimated uncertainties of 20% and 29%, respectively.
translated into an error in the determined rate constant. In that
respect, photolytic decomposition of various precursors fre-
quently fails as a “clean” source of radicals, especially when
radicals in question contain more than one or two carbon atoms
and at elevated temperatures (e.g., ref 5). A successfully used
alternative is pulsed production of chlorine or fluorine atoms that
are made to quickly react with a corresponding hydrocarbon to
produce the desired radicals (e.g., refs 5ꢀ8). In the current study,
the reaction between Cl atoms and cyclohexane is used as a
“clean” source of cyclohexyl radicals, and the second product of
this reaction, HCl, serves as a nonreactive (under the conditions
of experiments performed in this work) measure of the amount
of radicals produced.
I. INTRODUCTION
Radicalꢀradical reactions are important elementary steps in
the combustion and pyrolysis of hydrocarbons.1,2 These reac-
tions generally, although not without exceptions, serve as chain
termination pathways. Knowledge of the rate constant and the
channel branching ratio of such reactions is necessary for
accurate modeling of the combustion of organic fuels. Despite
their importance, information available on the rates of these
reactions is sparse and often controversial as radicalꢀradical
reactions are difficult to study experimentally due to the high
reactivity of the species involved. Because of the difficulties
encountered in experimental studies, theoretical methods of
evaluating and predicting rates of radicalꢀradical reactions
become ever more important, and recent advancement of
theoretical methods holds great promise (e.g., refs 3 and 4 and
references cited therein). Further development and validation of
theoretical methods requires a set of accurately measured
experimental data on a variety of benchmark reactions, preferably
obtained in direct experiments. Such a database is generally
lacking, and in particular there is a scarcity of rate data for the
reactions between relatively large radicals.
Experimental difficulties in direct experimental studies of
radicalꢀradical kinetics are generally caused by two factors.
One is the difficulty in creating requisite radicals in the gas phase
without at the same time creating some other undesired reactive
species, the reactions of which may interfere with the subsequent
kinetics of the radicals under study. The second factor is the
difficulty in determining the initial concentrations of the radicals
formed, as any potential error in signal calibration is directly
The self-reaction of cyclohexyl radicals
c-C6H11 þ c-C6H11 f C12H22 ðbicyclohexylÞ
ð1aÞ
ð1bÞ
f c-C6H10 þ c-C6H12
can proceed via recombination (channel 1a) or disproportiona-
tion (channel 1b). The recombination-to-disproportionation
branching has been studied before by several groups.9ꢀ12 All
studies used gas chromatography or gas chromatographyꢀmass
spectrometry to analyze final products. The range of reported
values of branching fractions of the disproportionation channel
Received: April 29, 2011
Revised:
June 17, 2011
Published: June 26, 2011
r
2011 American Chemical Society
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1b is 31ꢀ54% and the experimental temperatures are from 302
to 475 K.
of radicals can be determined with a high degree of accuracy. In
the current study, the method of Baklanov and Krasnoperov7 was
used to generate cyclohexyl radicals. This method is based on
using the 193 nm photolysis of oxalyl chloride ((CClO)2) with
consecutive conversion of Cl atoms to radicals of interest (R) and
HCl by a fast reaction with a suitable substrate:
Two experimental determinations of the rate constant of
reaction 1 are available in the literature. Currie et al.10 in 1974
obtained an upper limit of 1.7 ꢁ 10ꢀ14 cm3 moleculeꢀ1 sꢀ1 for
the rate constant of the recombination channel (1a) using
360 nm photolysis and final product analysis. Combined with
the branching ratio of k1b/k1a = 0.99 reported in the same paper,
this results in the upper limit of ∼3 ꢁ 10ꢀ14 cm3 moleculeꢀ1 sꢀ1
for the rate constant of the overall reaction. In 1999, Platz et al.6
used pulsed radiolysis of SF6/cyclohexane mixtures to create c-
C6H11 and UV absorption to monitor their kinetics in real-time
experiments. These authors obtained the value of k1 = (3.0 (
0.4) ꢁ 10ꢀ11 cm3 moleculeꢀ1 sꢀ1 at 296 K and the pressure of
700 Torr of nitrogen.
In this work, we present the results of the first direct real-time
experimental investigation of the temperature dependence of the
kinetics of the self-reaction of cyclohexyl radicals. Reaction 1 was
studied by Laser Photolysis/Photoionization Mass Spectrome-
try. Overall rate constants of reaction 1 were obtained in the
temperature interval 303ꢀ520 K and bath gas (helium with up to
5% of radical precursors) densities in the range (3.00ꢀ12.0) ꢁ
1016 molecules cmꢀ3. The branching fraction of channel 1b was
obtained at room temperature and a bath gas density of 12.0 ꢁ
1016 molecules cmꢀ3. The article is organized as follows: section
II presents the experimental methods and the results of the
determinations of the rate constants and the branching fraction
of disproportionation, and a discussion is presented in section III.
193 nm
ðCClOÞ2
s
2C1 þ 2CO
ð2aÞ
ð2bÞ
ð3Þ
f
f Cl þ CO þ CClO f 2Cl þ 2CO
Cl þ RH f R þ HCl
The 193 nm photolysis of oxalyl chloride serves as a “clean”
photolytic source of chlorine atoms (“clean” in the sense that no
other reactive species are produced by the photolysis). Since the
yield of chlorine atoms in reaction 2 is exactly 200%, the initial
concentration of Cl (and, consequently, that of R) can be
determined either from the extent of the photolytic depletion of
oxalyl chloride8,15 or from the measured production of HCl.8 The
equivalence of the two methods of evaluating the initial concen-
tration of Cl and R has been experimentally confirmed before.8 In
the experiments on the kinetics of reaction 1, the 193-nm
photolysis of (CClO)2 followed by the subsequent fast reaction
of the Cl atoms with cyclohexane was used as a source of
cyclohexyl radicals. Production of HCl was used to determine
the initial concentrations of c-C6H11. Measured flows of (gaseous)
HCl were used for calibration of the HCl ion signal. Concentra-
tions of cyclohexane ((2.0ꢀ11) ꢁ 1014 molecules cmꢀ3) were
selected to ensure a virtually instantaneous (on the time scale of
the reactions studied) conversion of Cl into cyclohexyl radicals
and HCl. The rate constant of reaction 3 is unknown but can be
estimated at (2ꢀ3) ꢁ 10ꢀ10 cm3 moleculeꢀ1 sꢀ1 by analogy with
the reactions of chlorine atoms with other alkanes (e.g., ref 16).
The rate of the reverse reaction, that of c-C6H11 with HCl, is
negligibly small under the conditions of the current study, as can
be expected on the basis of the known kinetics of the reaction of
methyl radical with HCl (rate constants in the range (0.5ꢀ1.2) ꢁ
10ꢀ13 cm3 moleculeꢀ1 sꢀ1 between 300 and 495 K17). The
observed temporal profiles of the HCl signal were flat during
the 0ꢀ30 ms monitoring time, with temporal resolution deter-
mined by the per-channel dwell time of the multichannel scaler
(0.1 ꢀ 0.3 ms). Separate experiments were performed to verify
that no cyclohexyl radicals were produced by the photodissocia-
tion of cyclohexane in the absence of oxalyl chloride.
Radical precursors and other chemicals used (see below) were
obtained from Aldrich (oxalyl chloride, g99%, cyclohexane,
99.9%), Alpha Aesar (cyclohexene, 99%), Matheson (HCl,
99.99%), Fisher Scientific (benzene, g99%), and Roberts Oxy-
gen (helium, 99.999%, less than 0.0002% of oxygen). Oxalyl
chloride, cyclohexane, cyclohexene, and benzene were purified
by vacuum distillation prior to use. Helium and hydrogen
chloride were used without further purification.
Determination of the Rate Constant. The kinetics of the
cyclohexyl radical decay was monitored in real time. Rate
constant measurements were performed using a technique
applied by us earlier to the studies of the self-reactions of
ethyl5 and propargyl8 radicals, which, in turn, is based on the
method used by Slagle and co-workers18 in their study of the
CH3 + CH3 reaction. The experimental conditions were selected
in such a way that the characteristic time of the reaction between
Cl and cyclohexane was at least 300 times shorter (typically, 1000
II. EXPERIMENTAL SECTION
Apparatus. Details of the experimental apparatus have been
described previously;13 only a brief description is given here.
Pulsed 193 nm unfocused light from a Lambda Physik 201 MSC
excimer laser was directed along the axis of a heated 50-cm-long
tubular reactor (i.d. 1.05 cm). The reactor surface was coated
with boron oxide to reduce radical wall losses.14 The laser was
operated at 4 Hz and a fluence of 10ꢀ80 mJ pulseꢀ1. In order to
replace the photolyzed gas mixture with fresh reactants between
laser pulses, the flow of the gas mixture containing the radical
precursors and the bath gas (helium) was set at ∼4 m sꢀ1. The
mixture was continuously sampled through a small tapered
orifice in the wall of the reactor and formed into a beam by a
conical skimmer before entering the vacuum chamber containing
the photoionization mass spectrometer. As the gas beam tra-
versed the ion source, a portion was photoionized by an atomic
resonance lamp, mass selected by a quadrupole mass filter, and
detected by a Daly detector. Temporal ion signal profiles were
recorded from a short time before the laser pulse (10ꢀ30 ms) to
15ꢀ30 ms following the pulse by a multichannel scaler interfaced
to a PC computer. Typically, data from 500 to 30 000 repetitions
of the experiment were accumulated before the data were
analyzed. The sources of the photoionization radiation were
chlorine (8.9ꢀ9.1 eV, CaF2 window, used to detect c-C6H11, c-
C6H10, and benzene), hydrogen (10.2 eV, MgF2 window, used to
detect C12H22), and neon (16 eV, collimated hole structure, used
to detect HCl, benzene, and (CClO)2) resonance lamps.
Radical Generation. Real-time experimental studies of radical
self-reactions, ideally, require a suitable pulsed source of radicals
that should satisfy two requirements: (1) that the radicals of
interest are the only reactive species present in the reactor during
the kinetics of radical decay and (2) that the initial concentration
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presence of heterogeneous loss, the line is curved, the initial slope
is proportional to (2k0 + k4), and the deviation from a straight line
can serve as a measure of the contribution from the heteroge-
neous wall loss. As can be seen from the plot in Figure 1 (also, a
full-sized plot of the same dependence is given in the Supporting
Information), both the slope of the initial part of the reciprocal
signal versus time dependence and the slight deviation from
linearity are well characterized, which illustrates that both the
k1[R]0 and the k4 values can be obtained from the fit of the signal
with a high degree of accuracy. Constraining the values of k4 to the
upper or lower limits of the resultant uncertainty ranges (1σ)
generally resulted in fitted k1[R]0 values corresponding to the
respective lower or upped error limits of the unconstrained fit.
The rate of the heterogeneous loss of radicals (reaction 4) did
not display any dependence on the laser intensity or concentra-
tions of the radical precursors, but was affected by the condition of
the walls of the reactor, such as the history of exposure to different
reacting mixtures. In principle, it was possible to obtain the rate
constants of the heterogeneous loss of radicals, k4, in separate
experiments with low initial radical concentrations selected in
such a way as to make the rates of radical self-reactions negligible.
However, in the experiments performed to determine the rates of
the c-C6H11 self-reaction (with high cyclohexyl concentrations), a
small fraction of the Cl atoms produced in the photolysis of oxalyl
chloride decayed on the reactor walls, which could possibly have
affected the wall conditions. Thus, it was deemed more appro-
priate to determine the rates of wall losses of radicals in the same
experiments where the rates of radical self-reactions were ob-
tained. Separate experiments with low cyclohexyl concentrations
(such that the c-C6H11 self-reaction was negligible) were per-
formed to confirm that the values of k4 obtained (19ꢀ25 sꢀ1) are
in general agreement with those derived from the three-parameter
fits of radical decays obtained with high c-C6H11 concentrations
(5ꢀ24 sꢀ1). A reaction of the cyclohexyl radicals with oxygen
impurity in the helium carrier gas may be a potential concern.
However, under the experimental conditions used, the concen-
tration of oxygen was less than 2.4 ꢁ 1011 molecules cmꢀ3 (7ꢀ40
times lower than the initial concentrations of cyclohexyl), which
makes any contribution of the c-C6H11 + O2 reaction to the
overall kinetics of cyclohexyl decay negligible, especially consider-
ing the corresponding rate constant values of less than 1.7 ꢁ
Figure 1. The k1[c-C6H11]0 versus [c-C6H11]0 dependence obtained in
the study of reaction 1 at room temperature. Circles: bath gas density of
12.0 ꢁ 1016 molecules cmꢀ3; squares: bath gas density of 3.0 ꢁ 1016
molecules cmꢀ3. Upper left inset shows a typical temporal c-C6H11 ion
signal profile recorded in an experiment to determine the rate of the c-
C6H11 + c-C6H11 reaction. The conditions are those of the filled circle
on the main plot; the white solid line is the result of the fit with eq I. The
lower right inset shows the reciprocal of the c-C6H11 ion signal as a
function of time (also given in full size in the Supporting Information,
Figure 1S). The observed slight deviation from linearity is due to the
minor heterogeneous loss of radicals in reaction 4, as discussed in text.
times shorter) than that of the self-reaction of the cyclohexyl
radicals. Under these experimental conditions, the self-reaction
of c-C6H11 was unperturbed by any side processes and the only
additional sink of the radicals was due to the heterogeneous wall
loss, which was taken into account in the analysis. Thus, the
experimental kinetic mechanism included reactions
c-C6H11 þ c-C6H11 f products
c-C6H11 f wall loss
ð1Þ
ð4Þ
For this kinetic mechanism and initial conditions described
above, the corresponding first-order differential equations can be
solved analytically:
S0 k4
3
10ꢀ11 cm3 moleculeꢀ1 sꢀ1 20
.
S ¼
ðIÞ
ð2k0 þ k4Þ ek t ꢀ 2k0
4
3
In each experiment, the initial concentration of the cyclohexyl
radicals was determined by measuring the production of HCl
relative to a calibration standard. This value was obtained directly
from the HCl+ ion profile. In each experiment to determine k0 =
k1[R]0, the production of HCl was measured two times (before
and after the kinetics of the radical decay was recorded).
For each experimental temperature, the initial radical concen-
tration [R]0 (R = c-C6H11), was varied by changing the con-
centration of oxalyl chloride and/or the laser fluence. The values
of the k1[R]0 product obtained from the data fits were plotted as a
function of the initial concentration of radicals obtained from the
measurements of the photolytic production of HCl ([R]0). The
values of the radical self-reaction rate constant were determined
from the slopes of the linear k1[R]0 versus [R]0 dependences.
The regression fits were constrained to pass through the center of
coordinates; however, unconstrained linear fits resulted in inter-
cept values that were ∼3 times smaller than the corresponding
standard errors of the fit.
Here, k0 = k[R]0, k1 and k4 are the rate constants of reactions 1
and 4, respectively, [R]0 is the initial radical concentration, S is
the radical ion signal, and S0 is the signal amplitude. In each
experiment, the values of the signal amplitude S0, the wall loss
rate k4, and the k1[R]0 product were obtained from the fits of the
real-time radical decay profile with eq I. A typical signal profile of
the cyclohexyl radical decay is shown in Figure 1 (upper inset).
Different parts of the radical decay profiles exhibit different
sensitivities to the fitting parameters. The initial part of the signal
profile is most sensitive to the rate constant of the radical self-
reaction, whereas the end part is most sensitive to the rate
constant of the heterogeneous wall loss of the radicals. These
sensitivities are illustrated in the lower inset in Figure 1, where the
reciprocal of the radical signal (with the baseline determined
before the photolyzing laser pulse subtracted) is plotted as a
function of time. In the absence of any heterogeneous wall loss of
radicals (pure second-order decay) the reciprocal signal is directly
proportional to time and forms a straight line; the self-reaction
rate constant can be obtained from the slope of the line. In the
The values of the rate constant of reaction 1 were obtained at
303 ((4), 400, and 520 K. The upper experimental temperature
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with the following Arrhenius expression:
k1 ¼ 4:8 ꢁ 10ꢀ12 expð þ 542 K=TÞ cm3 moleculeꢀ1sꢀ1 ð303ꢀ520 KÞ
ðIIÞ
Estimated uncertainty associated with this expression is 16%
throughout the above temperature range.
Product Analysis. Formation of both C12H22 (m/z = 166)
and C6H10 (m/z = 82) was observed in real-time experiments,
with the characteristic rise times matching those of the cyclohexyl
decay due to reaction 1; these products were attributed to
reaction channels 1a and 1b, respectively. An example of a
C6H10 growth profile and the corresponding C6H11 decay is
given in the Supporting Information. It was not possible to
measure the ratio of these two products because of the difficulty
in calibrating the sensitivity of the apparatus to C12H22 due to the
very low vapor pressure of the latter. Instead, experiments to
determine the ratio of the C6H10 product concentration to the
amount of HCl produced in reaction 3 were performed. These
experiments were complicated by the fact that the intensity of the
chlorine photoionizing lamp used to detect C6H10 changed with
time because of decreasing transparency of the CaF2 windows
during the experiment. To circumvent this problem, benzene was
used as an internal standard. Measured low concentrations of
benzene ((0.2ꢀ1.4) ꢁ 1013 molecules cmꢀ3, at least 18 times
lower than the concentrations of cyclohexane to ensure that any
potential contribution of the Cl + C6H6 reaction is negligible)
were added to the reactive mixtures. The cyclohexene-to-ben-
zene (with the chlorine lamp) and benzene-to-HCl (with the
neon lamp) sensitivity ratios were determined experimentally
using known concentrations of these species. Experiments were
performed to verify that no photolysis of benzene occurs to any
measurable extent. Recorded temporal profiles of the C6H10
signal were fitted with a rising function obtained by numerical
integration of the differential equation d[C6H10]/dt = ꢀk1b[c-
C6H11]2, where [c-C6H11] is given by eq I, using the branching
fraction of disproportionation γ(1b) = k1b/(k1a + k1b) as the
fitting parameter. The results are presented in Table 2. The
quoted values of [c-C6H10]∞ given in the table are the infinite-
time concentrations obtained by multiplying the initial radical
concentration by the values of γ(1b).
Figure 2. The k1[c-C6H11]0 versus [c-C6H11]0 dependences obtained
in the study of reaction 1 at 400 K (open circles and dashed line) and
520 K (filled circles and solid line).
was determined by the expected onset of the isomerization
reaction proceeding via ring-opening and producing the methyl-
cyclopentyl radical.19,20 For this purpose, the value of 10 sꢀ1
(similar to the typical rate of radical wall loss) was selected as the
acceptable upper limit of the isomerization rate constant.
RRKM/Master equation21,22 calculations were performed to
estimate isomerization rate constants using the G2(MP2)-level
potential surface for cyclohexyl isomerization from the theore-
tical study of Knepp et al.20 Calculations were performed using
the ChemRate program.23 The somewhat high value of the
average energy transferred per deactivating collision, ÆΔEædown
=
500 cmꢀ1, was used, as it is safer to err on the higher side. The
resultant isomerization rates were less than 1.4 sꢀ1 at the
experimental pressures and the highest temperature used in the
current work, 520 K. A potential error in the energy barrier of
2 kcal molꢀ1 would result in a change of the isomerization rate
constant at this temperature by a factor of 6.4. Thus, the upper
limit of the isomerization rate at 520 K can be estimated at
∼10 sꢀ1, which is significantly lower that the rates of cyclohexyl
decay due to reaction 1. Hence, 520 K was selected as the upper
temperature limit of the experiments.
The bath gas densities (helium with up to 5% of radical
precursors) of 3 ꢁ 1016 and 12 ꢁ 1016 molecules cmꢀ3 were
used in the room-temperature experiments and the density of
12 ꢁ 1016 molecules cmꢀ3 was used at 400 and 520 K. Experi-
mental parameters such as the photolyzing laser intensity and the
concentrations of oxalyl chloride and cyclohexane were varied
for individual experiments. For each temperature, the values of
the k1[R]0 product obtained under different experimental con-
ditions (including different bath gas densities) are shown on the
same k1[R]0 versus [R]0 plots in Figures 1 and 2. The rate
constant of the cyclohexyl radical self-reaction does not demon-
strate any dependence (within the experimental uncertainties)
on the parameters varied; no pressure dependence of k1 at room
temperature can be observed within the experimental uncertain-
ties. The conditions and the results of individual experiments are
presented in Table 1. The values of k1 determined from the
slopes of the k1[R]0 versus [R]0 dependences are also given in
Table 1 for the three experimental temperatures.
When branching fraction experiments were attempted at
temperatures of 400 and 520 K, enhanced signals at m/z = 36
were observed when benzene was present in addition to hydrogen
chloride, and a high-energy neon lamp with a collimated hole
structure window was used. This effect was tentatively attributed
to either production of HCl+ or C3+ in ionꢀmolecular reactions
+
in the ion source or to C3+ fragment of C6H6 . The latter could
have appeared as a result of ionization of benzene with the higher-
energy light from the neon lamp (unlike salt windows, the
collimated hole structure does not block any low wavelength
components) or from electron-impact ionization, with electrons
generated by photoelectric effect due to light impacting the ion
lenses. This m/z = 36 signal effectively prevented experiments on
the branching fraction of channel 1b at temperatures above
ambient. Thus, determination of the fraction of the reaction
channel 1b was limited to room temperature. The results of these
experiments are summarized in Table 2. The average value of the
channel 1b branching fraction is 41 ( 7%, where the uncertainty
includes 1σ random and systematic contributions. Attempts to
determine the higher-temperature branching ratio of reaction 1
via final product analysis by gas chromatography were undertaken
The values of the rate constant obtained in the experiments are
presented in Figure 3 as a function of temperature. A negative
temperature dependence is observed, which can be represented
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Table 1. Conditions and Results of Experiments to Determine k1
c
d
e
f
[M]a
Ib
[c-C6H12
]
[(CClO)2]c
[c-C6H11 0
]
k1[R]0
k4
Experiments at 303 ( 4 K. k1(303 K) = (2.89 ( 0.43g) ꢁ 10ꢀ11 cm3 moleculeꢀ1 sꢀ1
12.0
3.0
8.9
7.8
9.0
5.2
14
10
11
13
5.0
16
13
2.62
10.7
2.62
10.9
2.67
8.16
2.62
2.67
10.9
2.58
2.04
0.65
0.91
1.15
2.06
0.87
1.36
1.36
1.60
4.17
1.65
2.45
1.86 ( 0.57
2.29 ( 0.31
3.33 ( 0.62
3.43 ( 0.63
3.99 ( 0.81
4.43 ( 0.76
4.60 ( 0.47
6.49 ( 1.07
6.76 ( 0.87
8.40 ( 1.39
9.89 ( 0.87
58.1 ( 3.6
74.3 ( 9.5
88.5 ( 5.4
91.6 ( 5.9
103 ( 7
10.7 ( 1.3
22.7 ( 3.3
12.7 ( 0.8
13.4 ( 0.9
9.7 ( 0.8
12.0
3.0
12.0
12.0
12.0
12.0
3.0
132 ( 12
149 ( 15
179 ( 18
211 ( 28
237 ( 31
284 ( 52
10.1 ( 1.2
10.7 ( 1.5
11.0 ( 0.8
13.1 ( 1.3
10.8 ( 0.8
23.8 ( 1.5
12.0
3.0
Experiments at 400 K. k1(400 K) = (1.91 ( 0.28g) ꢁ 10ꢀ11 cm3 moleculeꢀ1 sꢀ1
12.0
12.0
12.0
12.0
12.0
12.0
3.1
2.4
2.3
3.2
3.2
2.9
2.94
2.49
5.81
2.76
2.97
2.95
2.19
4.15
6.36
5.65
8.36
9.44
2.15 ( 0.35
3.16 ( 0.32
4.66 ( 0.23
5.74 ( 0.26
8.71 ( 1.32
8.79 ( 0.56
42.7 ( 2.7
65.0 ( 5.1
101 ( 8
9.9 ( 1.5
11.2 ( 1.8
10.0 ( 1.5
10.8 ( 0.9
9.9 ( 1.8
5.3 ( 1.1
95.1 ( 6.2
149 ( 17
186 ( 21
Experiments at 520 K. k1(520 K) = (1.34 ( 0.17g) ꢁ 10ꢀ11 cm3 moleculeꢀ1 sꢀ1
12.0
12.0
12.0
12.0
12.0
12.0
2.1
2.6
2.3
2.7
2.2
3.3
2.58
2.75
2.75
2.85
3.01
3.09
1.85
2.52
4.56
6.92
5.52
8.24
1.81 ( 0.50
2.15 ( 0.05
3.34 ( 0.06
6.06 ( 0.69
3.82 ( 0.19
8.67 ( 0.45
19.1 ( 1.8
29.3 ( 1.7
38.5 ( 2.5
98.9 ( 6.9
53.8 ( 3.0
105.4 ( 9.8
14.1 ( 2.0
13.3 ( 1.2
11.6 ( 1.5
11.0 ( 1.0
12.6 ( 1.1
15.6 ( 1.8
a Concentration of the bath gas (helium with up to 5% of radical precursors) in units of 1016 molecules cmꢀ3. b Estimated laser fluence in units of mJ
pulseꢀ1 cmꢀ2. In units of 1014 molecules cmꢀ3
.
d Nascent concentration of cyclohexyl radicals in units of 1012 molecules cmꢀ3 determined from
c
production of HCl. e Obtained from the fits of the kinetics of the cyclohexyl decay with eq I. f Rate constant of the heterogeneous wall loss obtained from
the fits of the kinetics of the c-C6H11 decay with eq I. g Uncertainties are 1σ (statistical) + systematic.
Table 2. Conditions and Results of Experiments to Deter-
mine the Branching Fraction of Disproportionation in
Reaction 1a
b
c
d
T/K [c-C6H12
]
[(CClO)2]b [c-C6H11 0
]
[c-C6H10 ∞
]
γ(1b)e
305
305
306
2.54
2.54
2.51
1.56
2.50
5.32
2.08 ( 0.16 0.84 ( 0.07 40.4 ( 6.0%
3.20 ( 0.34 1.19 ( 0.11 37.2 ( 6.7%
5.76 ( 0.41 2.59 ( 0.20 45.0 ( 4.2%
a All quoted uncertainties are 1σ (statistical) + systematic. b In units of
1014 molecules cmꢀ3. c Nascent concentration of cyclohexyl radicals in
units of 1012 molecules cmꢀ3 determined from production of HCl.
d Concentration of cyclohexene extrapolated to infinite time (see text),
in units of 1012 molecules cmꢀ3. e Branching fraction of channel 1b.
final values of the rate constants and branching ratios using
different mathematical procedures for propagating systematic
and statistical uncertainties.24 The error limits of the values
reported in this work represent a sum of 1σ statistical uncertainty
and estimated systematic uncertainty, unless specified otherwise.
Figure 3. Temperature dependence of k1. Filled circles: current study;
open square: ref 6; wide horizontal line with a downward arrow: upper
limit of ref 10.
but failed because of the reaction between the remaining oxalyl
chloride and the gas chromatography column coating.
The sources of error in the measured experimental parameters
such as temperature, pressure, flow rate, signal count, etc. were
subdivided into statistical and systematic and propagated to the
III. DISCUSSION
This work presents the first direct real-time experimental
determination of the rate constant of the c-C6H11 + c-C6H11
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Figure 4. Temperature dependence of k1 (symbols and solid line, as in
Figure 3) compared with the temperature dependences of the rate
constants of the self-reactions of CH3 (dashed line, theory-based
parametrization of ref 4) and C2H5 (dotted line, ref 5).
Figure 5. Values of the branching fraction of the disproportionation
channel (1b) obtained at different temperatures. Filled solid circle:
current study; open square and open diamond: ref 9, values derived
from the initial product formation rates and from the steady-state
cyclohexene formation rate, respectively; open circles: ref 10; narrow
long rectangles with dashed and solid line borders: refs 11 and 12,
respectively. Straight dotted line: a least-squares linear fit to the tem-
perature dependence (see text).
reaction (k1) as a function of temperature (303ꢀ520 K). The
overall rate constant values obtained in the current study are in
agreement with the earlier room-temperature value of k1 reported
by Platz et al.6 (Figure 3). The 1.7 ꢁ 10ꢀ14 cm3 moleculeꢀ1 sꢀ1
upper limit given by Currie et al.10 for the rate constant of the
recombination channel1a and corresponding to the upper limit of
∼3 ꢁ 10ꢀ14 cm3 moleculeꢀ1 sꢀ1 for the overall reaction is more
than 2 orders of magnitude lower than the results of the current
study. This upper limit was obtained by the authors of ref 10 in
their analysis of the final products of a system of reactions
occurring during 360-nm photolysis of azocyclohexane in the
presence of carbon tetrachlorideand cyclohexane. The main focus
of that study was the kinetics of the reactions of cyclohexylradicals
with CCl4 and that of the CCl3 radicals with cyclohexane. Rates of
some of the reactions playing important roles in the experimental
system were unknown and had to be estimated by the authors.
The uncertainties of these estimates have likely affected the
resulting evaluation of k1b. In particular, a rather low upper limit
of 6.6 ꢁ 10ꢀ13 cm3 moleculeꢀ1 sꢀ1 to the preexponential factor of
the abstraction reaction of the cyclohexyl radicals with CCl4 was
assumed, which, combined with experimentally determined pro-
duct ratios, translated into a low value of 5 ꢁ 10ꢀ13 cm3
moleculeꢀ1 sꢀ1 for the upper-limit rate constant of the c-C6H11
+ CCl3 cross-combination reaction. The latter value was con-
verted into the k1a e 1.7 ꢁ 10ꢀ14 cm3 moleculeꢀ1 sꢀ1 upper limit
by using an experimentally determined cross-combination-to-
recombination products ratio of c-C6H11 and CCl3 and a litera-
ture value for the rate constant of CCl3 recombination.
It is interesting to note that the rate of reaction 1 demonstrates
rather strong negative temperaturedependence (Figures 3 and 4).
Figure 4 compares the temperature dependence of k1 with those
of the self-reactions of methyl and ethyl radicals, the only two alkyl
radical self-reactions for which directly determined temperature-
dependent rate constants are available in the literature. As can be
seen from the plot, within the 303ꢀ520 K temperature range, the
rate constant of reaction 1 decreases with temperature much
faster than the rates of self-reactions of the other two smaller
radicals. In that respect, reaction 1, with a negative activation
energy of ꢀ4.51 kJ molꢀ1 (E/R = ꢀ542 K, eq II), behaves in a
manner similar to that of the reactions of small alkyl radicals
(C2H5, n-C3H7, and n-C4H9) with CH3, which have reported
negative activation energies in the ꢀ3.93 to ꢀ1.62 kJ molꢀ1 range
(E/R between ꢀ473 K and ꢀ387).25 The difference between the
temperature dependence of reaction 1 and those of methyl and
ethyl radical self-reactions is in general agreement with the
observation by Klippenstein et al.4 that additional substituents
at the radical center and increasing steric bulk of radicals result in
stronger negative temperature dependences of their theoretically
calculated recombination rate constants.
Figure 5 presents the branching fraction of the disproportio-
nation channel (1b) obtained in the current study in comparison
with the values reported in or derived from the results of earlier
relative-rates studies, as explained below. The branching fraction
values are shown as a function of temperature.
In 1954, Beck et al.9 used mercury-photosensitized decomposi-
tion of cyclohexane at 302 K to produce cyclohexyl radicals and H
atoms under static reactor conditions and gas chromatography/
mass spectrometry to identify and quantify the products of the
subsequent reactions. The initial rates of product formation and
those obtained under steady-state conditions were determined;
the authors reported a value of 2.2 for the recombination-to-
disproportionation branching fraction obtained from the initial
rates. Using this value and the uncertainties given for the rates of
product formation in ref 9, one can obtain a value of 31 ( 6% for
the fraction of channel 1b (open square in Figure 5). The authors
comment that product formation rates of cyclohexene and hydro-
gen obtained experimentally under steady-state conditions are
somewhat lower than expected from the analysis of the initial rates.
Using the steady-state rate of cyclohexene formation within the
framework of the mechanism of ref 9 yields a higher value of the
disproportionation branching fraction, 45 ( 6% (calculated in the
current study), which is shown in Figure 5 with an open diamond.
In 1974, Currie et al.10 used 360 nm photolysis of mixtures of
azocyclohexane, carbon tetrachloride, and cyclohexane to pro-
duce c-C6H11 and gas chromatography and mass spectrometry to
analyze final products. Formation of both bicyclohexane and
cyclohexene, attributed to reactions 1a and 1b, was observed and
quantified. The authors did not use these results to evaluate the
branching ratio of reaction 1; instead, they referred in the article
to their earlier (apparently, unpublished) study in which the
disproportionation to combination ratio of 0.99 was obtained,
with no error limits given. Using the reported10 yields of C12H22
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and c-C6H10, one can obtain similar values (averaging to 0.94 at
T = 419ꢀ475 K), although with a positive temperature depen-
dence. Open circles in Figure 5 show the corresponding values of
the fraction of the disproportionation channel.
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In 1979, Fujisaki and G€aumann11 used radiolysis of water
vapor in the presence of cyclohexane and final analysis of products
by gas chromatography to determine the disproportionation-to-
combination ratio of reaction 1. The value of 0.56 ( 0.01 was
reported for the 343ꢀ443 K experimental range of temperatures.
In 1982, the same authors repeated their experiments using
somewhat different experimental conditions, as a part of their
study of self-reactions and cross-radical reactions involving cyclo-
hexyl and cyclopentyl radicals, as well as their deuterated
analogues.12 The temperature range of the second study was
more narrow (398ꢀ443 K), and the reported disproportiona-
tion-to-combination ratio value was 0.59 ( 0.02. The corre-
sponding values of the disproportionation branching fraction are
35.9 ( 0.4% and 37.1 ( 0.8% for the 1979 and the 1982 studies,
respectively. These envelopes of uncertainties are shown in
Figure 5 with thin long rectangles covering the associated
temperature ranges and framed with dashed and solid lines.
The values of the channel 1b branching fraction shown in
Figure 5 are in general agreement with each other, covering the
range of roughly 30ꢀ50%. The general trend, together with
the results of Currie et al. seems to suggest a weak positive
temperature dependence. Drawing a least-squares linear fit
through the data results in the following equation for the
disproportionation branching fraction: γ(1b) = 20 + 0.056 ꢁ
T %, shown in Figure 1 with a dotted line. However, the scatter of
the data exceeds variation in γ(1b) within the temperature range
covered by experiments due to this hypothetical trend, and thus it
may be preferable to use the room-temperature value of the
current study, 41 ( 7%, for all temperatures instead. The
corresponding temperature dependences of the recombination
and the disproportionation channels are
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(21) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and
Recombination Reactions; Blackwell: Oxford, 1990.
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Reactions, 2nd ed.; Wiley: New York, 1996.
(23) Mokrushin, V.; Bedanov, V.; Tsang, W.; Zachariah, M. R.;
Knyazev, V. D.; McGivern, W. S. ChemRate, version 1.5.8; National
Institute of Standards and Technology: Gaithersburg, MD, 2011
(http://kinetics.nist.gov/chemrate/).
kð1aÞ ¼ 2:8 ꢁ 10ꢀ12 expð þ 542 K=TÞ cm3 moleculeꢀ1 sꢀ1 ð303ꢀ520 KÞ
ðIIIÞ
kð1bÞ ¼ 2:0 ꢁ 10ꢀ12 expð þ 542 K=TÞ cm3 moleculeꢀ1 sꢀ1ð303ꢀ520 KÞ
ðIVÞ
(24) Colclough, A. R. J. Res. Natl. Bur. Stand. 1987, 92, 167.
(25) Knyazev, V. D.; Slagle, I. R. J. Phys. Chem. A 2001, 105, 6490.
with estimated uncertainties of 20% and 29%, respectively.
’ ASSOCIATED CONTENT
S
Supporting Information. A supplement, including a full-
b
sized plot of the dependence given in the lower right inset of
Figure 1 (Figure 1S) and an example of a C6H10 growth profile
and the corresponding C6H11 decay (Figure 2S). This material is
available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: knyazev@cua.edu.
’ ACKNOWLEDGMENT
This research was supported by the U.S. National Science
Foundation's Combustion, Fire, and Plasma Systems Program
under Grant No CBET-0853706.
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dx.doi.org/10.1021/jp204012w |J. Phys. Chem. A 2011, 115, 8616–8622