Kinetics of the Thermal Isomerization of 1,1-Dimethylcyclopropane

Article abstract of DOI:10.1002/kin.10008

Rate constants for the unimolecular thermal isomerization of gaseous 1,1-dimethylcyclopropane to isomeric methylbutenes have been measured, and Arrhenius parameters determined, over a wide temperature range, 683 - 1132 K, using a single-pulse shock tube and a static reactor. For the overall reaction, E_a = 61.8 +/- 0.4 kcal/mol, and log₁₀(A, s^-1) = 15.04 +/- 0.10. These values are in good agreement with previously reported values obtained over a much narrower temperature range. Rate constants for formation of the two major products, 2-methylbut-2-ene and 3-methylbut-1-ene, are given by E_a = 61.9 kcal/mol, logA = 14.80 and E_a = 61.1 kcal/mol, logA = 14.54, respectively. A comparison of the activation parameters for structural isomerizations of cyclopropane, methylcyclopropane, and 1,1-dimethylcyclopropane confirms a trend toward lower activation energy values as hydrogen atoms in cyclopropane are replaced by CH3 groups.

Full text of DOI:10.1002/kin.10008

Kinetics of the Thermal
Isomerization of
1,1-Dimethylcyclopropane
BANSI L. KALRA,1 DAVID K. LEWIS2
1
2
Received 24 July 2001; accepted 24 August 2001
ABSTRACT: Rate constants for the unimolecular thermal isomerization of gaseous 1,1-
dimethylcyclopropane to isomeric methylbutenes have been measured, and Arrhenius pa-
rameters determined, over a wide temperature range, 683–1132 K, using a single-pulse shock
tube and a static reactor. For the overall reaction, a = 61.8 0.4 kcal/mol, and log10( ,
s
1) = 15.04 0.10. These values are in good agreement with previously reported values ob-
tained over a much narrower temperature range. Rate constants for formation of the two
major products, 2-methylbut-2-ene and 3-methylbut-1-ene, are given by a = 61.9 kcal/mol,
log = 14.80 and a = 61.1 kcal/mol, log = 14.54, respectively. A comparison of the activa-
tion parameters for structural isomerizations of cyclopropane, methylcyclopropane, and 1,1-
dimethylcyclopropane confirms a trend toward lower activation energy values as hydrogen
C
atoms in cyclopropane are replaced by CH3 groups. 2001 John Wiley & Sons, Inc. Int J Chem
Kinet 33: 853–858, 2001
family of related cyclopropanes, then the ability of cal-
culational methods to deal correctly with the effects of
the substituents on bond energies and transition state
structures can be tested. For this reason, we have been
studying the kinetics of thermally induced reactions of
a series of methyl-substituted cyclopropanes. Through
the combined use of a single-pulse shock tube and static
reactors, we have obtained rate data over temperature
ranges of many hundreds of degrees, with reaction half-
lives ranging from fractions of a millisecond to many
days.
While many alkylcyclopropane isomerizations have
been studied previously in one or the other type of reac-
tor, the kinetic data for the much wider range of temper-
atures obtained by combining the static-reactor and the
shock-tube results allow us to evaluate the Arrhenius
parameters of competing isomerization and/or decom-
position channels with improved precision. For ex-
ample, in a reinvestigation of methylcyclopropane
INTRODUCTION
Mechanistic details of the structural and geometric iso-
merizations of cyclopropane have been of considerable
interest; the relative simplicity and high symmetry of
cyclopropane lends itself readily to examination of pos-
sible transition state structures by ab initio calculations,
affording a comparison of theory with experiment.
Adding simple substituents, such as methyl groups, to
the cyclopropane ring causes significant changes in the
activation parameters for isomerization. If these pa-
rameters can be determined with high accuracy for a
Correspondence to: David K. Lewis; e-mail: dklew@conncoll.
edu.
Contract grant sponsor: NSF.
Contract grant number: CHE 9714356.
Contract grant sponsor: Connecticut College.
Contract grant sponsor: Hollins University.
c
2001 John Wiley & Sons, Inc.

854
KALRA AND LEWIS
isomerization to four isomeric butenes [1], while we
confirmed the previously reported experimental acti-
vation parameters for isomerization to 1-butene and 2-
methylpropene, we also found that there is a definite but
much smaller difference in activation energies for the
formation of cis- and trans-2-butenes than that reported
in earlier studies. This difference in activation energies
has been essentially ignored by the many persons who
have worked to understand the mechanistic details of
cyclopropane isomerizations, over the 40 years since it
was first reported.
This paper describes the homogeneous, gas phase
isomerization kinetics of 1,1-dimethylcyclopropane
(DMCP). The first detailed rate studies on this
compound were reported by Flowers and Frey [2]
during 1959–1962. The heating of DMCP in an
“aged” reaction vessel at 720–784 K and at 715–754 K
produced mainly 3-methylbut-1-ene (3M1B) and
2-methylbut-2-ene (2M2B) in almost equal amounts.
These products can be readily accounted for by a
mechanism involving a C C bond fission to form a
diradical, followed by a 1,2 H transfer of a secondary
hydrogen:
that 2M1B is formed on reactor surfaces from the pri-
mary products. They also demonstrated (a) the absence
of a significant deuterium kinetic isotope effect on the
rate of isomerization, and (b) that neither carbene inter-
mediates nor methyl-group transfers are significantly
involved in the isomerizations of DMCP.
While a great deal is known already about the rates
and mechanisms of DMCP structural isomerizations,
the only specific determination of the activation pa-
rameters is from the rate studies of Flowers and Frey
[2], which covered a temperature range of 70 K. Im-
proved confidence limits in the activation parameters
are needed if they are to be quantitatively compared
withthoseforisomerizationsofcyclopropaneandother
alkylcyclopropanes. In the present study, we have re-
visited and extended the investigation of the kinetics
of structural isomerization of DMCP to a much larger
temperature range, 683–1132 K, using a single-pulse
shock tube and a static reactor.
EXPERIMENTAL SECTION
Materials
1,1-Dimethylcyclopropane was provided to us by J.E.
Baldwin at Syracuse University, who has described
the method of preparation previously [3]. CP grade
3M1B was obtained from Matheson Gas Products, and
2M2B (>99%) and 2M1B (>98%) were purchased
from Aldrich. These were used for the preparation of
reaction or calibration mixtures and for gc identifica-
tion of the products. Matheson CP grade cyclopropane
(CP) was added to DMCP–argon reactant mixtures to
serve as an internal temperature-probe. Liquid reagents
were degassed through multiple freeze-pump-thaw cy-
cles before use; gases from lecture bottles were used as
supplied. HP grade Helium was used as the driver gas
for the shock-tube runs.
Small quantities of 2-methylbut-1-ene (2M1B) were
also reported; this product cannot be accounted for
by the above mechanism. The overall isomeriza-
tion was found to be a homogeneous, unimolecu-
lar, first-order reaction, with Ea = 62.6 kcal/mol and
log10(A, s 1) = 15.05 for the overall isomerization to
all products.
Sample Preparation
Citing the isomerization of DMCP as “a verita-
ble fixed point in related hydrocarbon thermal re-
arrangement chemistry shown by other alkyl- and
dialkyl-substituted cyclopropanes” as the need for a
re-examination, Baldwin and Shukla [3] heated DMCP
and 1,1-dimethyl-2,2-d2-cyclopropane in a Pyrex bulb
at 693 K for various lengths of time and found the
same products as those observed by Flowers and Frey,
and a value for the rate constant comparable to the
one expected from the Arrhenius parameters reported
by the latter. They also showed that 3M1B and 2M2B
are the primary isomerization products of DMCP, and
Reaction mixtures for both the shock-tube and the
static-reactor runs were prepared by transferring into
a 1-L glass storage bulb, known pressures of degassed
DMCP and CP and diluting the mixture with Matheson
Research Grade (>99.9999%) argon. Calibration mix-
tures containing known percentages of 3M1B, 2M2B,
2M1B, and/or DMCP in argon were prepared in the
same way. The gas mixtures were thoroughly mixed
before use. The reactant mixture for the shock-tube
work contained 2.0% DMCP and 2.1% CP, while sam-
ples of a 2.99% DMCP/2.19% CP mixture were heated
in the static reactor.

KINETICS OF THE THERMAL ISOMERIZATION OF 1,1-DIMETHYLCYCLOPROPANE
855
Table I Summary of Reaction Conditions
Apparatus
Shock Tube
Static Reactor
A detailed description and operating procedures for
the shock tube and the static reactor used in this study
were reported earlier [4]. The high temperature runs
were carried out in a 2.54-cm diameter single-pulse
shock tube. Immediately after each sample of reac-
tant was shock-heated, two samples of product gases
were collected for analysis on a Varian 1440-20 gas
chromatograph. One of the samples, used to deter-
mine the relative amounts of the three product methyl-
butenes and unreacted DMCP, was separated on a 5%
n-octane on Poracil C column, 2 m in length, at 38 C.
The second sample, used to determine the reaction
temperature, was analyzed for the relative amounts of
unreacted CP and its isomerization product propene,
using a 4-m column containing 20% polypropylene
glycol saturated with AgNO3 on 80–100 mesh Chro-
mosorb W at room temperature. The static reactor used
for runs at lower temperatures consisted of a well-
aged 100 cm3 Pyrex cell surrounded by an aluminum
furnace, equipped with an Omega 650-J-D digital
thermometer.
Mixture
composition
Reaction
pressure
Reaction
temperature
2.0% DMCP/
2.1% CP
1.6–1.8 atm
2.99% DMCP/
2.19% CP
0.39–1.82 atm
1015–1132 K
683–734 K
Calculations
For the CP → propene reference reaction, rate con-
stants were calculated assuming irreversible first-order
kinetics; then the temperatures corresponding to those
rates were calculated using the well-established Ar-
rhenius parameters Ea = 65.00 kcal/mol and log10 (A,
s
1) = 15.20 for this reaction [6]. Gas chromatograph
peak heights for DMCP and its isomerization products,
corrected for measured sensitivity differences, were
used to determine the extent of the reaction DMCP
→ methylbutenes. The overall reaction rate constants
were calculated from the extent of production of the
three methylcyclobutenes, again assuming irreversible
first-order kinetics.
Kinetic Runs
For the high temperature runs, 45–60 Torr samples of
the reaction mixture containing DMCP, CP, and argon
diluent were introduced into the driven section of the
shock tube, and the shock wave was generated by filling
the driver section of the tube with helium to a pressure
sufficient to break the aluminum diaphragm separating
the two sections. The two product samples collected
from the downstream end of the shock tube were taken
sequentially, first a 25-cm3 sample and then a 200-cm3
sample. Both samples contained products formed at
the same reaction temperature but with different dura-
tions of heating, with the first collected sample hav-
ing been heated for about 800 ␮s, and the second for
an average of 600 ␮s [5]. The temperatures achieved
in these runs, as calculated from the CP/propene ratio
in the 25-cm3 product sample, ranged from 1015 to
1132 K.
For the runs at the lower temperatures, 127–551
Torr samples of reaction mixture were introduced
into the static reactor and heated for times ranging
from 25 to 30 min. At the end of the reaction time
25-cm3 samples of product mixtures were collected
and analyzed on the GC, for the CP/propene ratios
and for the relative amounts of methylbutene prod-
ucts and unreacted DMCP. The temperatures deter-
mined for these static-reactor runs varied from 683
to 734 K. Experimental conditions are summarized in
Table I.
RESULTS AND DISCUSSION
From the shock-tube heating, the only products of
DMCP isomerization observed were 2-methylbut-2-
ene (2M2B) and 3-methylbut-1-ene (3M1B), in all but
the one highest temperature (1132 K) and largest ex-
tent of conversion (56.3%) run from which some 2-
methylbut-1-ene (2M1B) was obtained, amounting to
4.5% of the total methylbutene products. When DMCP
was heated in the static reactor, 2M2B and 3M1B were
again the major products, but 2M1B was found in all
runs, in amounts that ranged from 3 to 25% of the
methylbutenes, with the percentage rising with extent
of conversion of DMCP to products.
In the products of the shock-tube runs, the ratios
of 2M2B to 3M1B ranged from 1.21:1.00 to 1.26:1.00,
except for the one run that produced measurable 2M1B,
in which the 2M2B to 3M1B ratio was 1.48:1.00. For
the static-reactor products, these ratios were 1.02:1.00
( .01) for runs which produced less than 5% 2M1B,
but increased up to 1.79:1.00 for the run which pro-
duced the largest amount of 2M1B, 25%. These ob-
servations suggest that 3M1B is the dominant precur-
sor of 2M1B. Baldwin and Shukla [3] provided exten-
sive evidence that the 2M1B they observed was pro-
duced by surface-catalyzed reactions, and they offered
possible mechanisms. That would explain the 2M1B

856
KALRA AND LEWIS
produced in our static reactor, but not that observed
in the products of the highest temperature shock-tube
run, in which the homogeneity of the process precluded
production of products on the reactor surface. In that
case, the most plausible explanation is a 1,4 H transfer
of a primary hydrogen to the methylene carbon, a pro-
cess suggested by Flowers and Frey but never shown
conclusively to take place in isomerization of gaseous
cyclopropanes.
The least-squares calculations for the activation en-
ergy and Arrhenius pre-exponential factor take into ac-
count random, but not systematic, errors. A potential
source of systematic errors in this and other studies in-
volving the use of the single-pulse shock-tube arises
in determining the reaction time, the length of time
the reactant sample was exposed to the high tempera-
ture/pressure conditions. Any error in the estimated re-
action time will affect the calculated rate constants and,
therefore, the Arrhenius parameters; a 50 ␮s reaction
time error in the shock-tube data, when combined with
the data from the static-reactor runs, would change the
deduced value of the activation energy by 0.3 kcal/mol
and the log A value by 0.10.
Figure 1 shows a plot of log10(k, s 1) as a function of
inverse temperature, where k is the first-order rate con-
stant for the overall isomerization of DMCP to all three
methylbutene isomers, for both the shock-tube and the
static-reactor runs. A linear least-squares fit for the
dataleadstotheArrheniusparameters: Ea = 61.8 0.4
kcal/mol; and log10(A, s 1) = 15.04 0.10. The un-
certainties listed here represent one standard deviation
in the linear regression; uncertainties at the 95% con-
fidence level are twice as large. Virtually identical val-
ues are obtained from a least-squares reduction of the
shock-tube data alone: Ea = 60.8 kcal/mol; log10(A,
Another potential source of systematic error in this
study is the assumption that both the reference reac-
tion and the subject isomerizations are at their high
pressure, first-order limits. Any error introduced by
this assumption should be lessened due to the struc-
tural similarity of DMCP and CP; indeed, in the earlier
study of methylcyclopropane isomerization, in which
CP was used as the internal thermometer, wide vari-
ations in reactant percentages failed to produce any
discernible mixture-to-mixture differences in rate con-
stants deduced for the four competing methylcyclo-
propane isomerizations [1]. In another previous study,
CP isomerization rates were measured via the compar-
ative rate shock-tube technique vs. cyclohexene retro
Diels–Alder decomposition [4a]. CP isomerization rate
constants were found to be depressed below the high
pressure limit by a factor of 0.4–0.7. However, al-
though total pressures in the reaction zone in that study
were similar to those of the present study, total or-
ganic molecule loading in the reactant samples was
0.2–0.4%, a factor of 10–25 less than total DMCP plus
CP pressures under reaction conditions in the present
study. This means that, in the present study, collisions
of DMCP or CP molecules with another strong col-
lider were 100–400 times as frequent as in the earlier
study. That said, it is understood that if there was any
retardation of reaction rates due to unimolecular fall-
off, it would likely have affected the CP isomerization
slightly more than the DMCP isomerizations with the
error being most significant in the high temperature
experiments. The resulting error would have led to re-
duced temperatures in the shock-tube runs, that were
a few degrees lower than the true temperatures, which
would in turn have led to deduced activation energies
for the DMCP isomerization, that are slightly higher
than the true values. This would have reduced the ap-
parent difference between the activation energies for
isomerization of DMCP and CP.
s
1) = 14.84. Also shown in Fig. 1 for comparison are
the rate constants reported by Flowers and Frey [2a]
for total isomerization of DMCP.
Comparing the 2M2B to 3M1B ratios from the
high and low temperature runs that produced lit-
tle or no 2M1B, we deduce separate sets of acti-
vation parameters from the parameters for the over-
all isomerization and the fraction of each prod-
uct formed at high and low temperatures: for
DMCP → 2M2B, Ea = 61.9 kcal/mol, log A = 14.80;
and for DMCP → 3M1B, Ea = 61.1 kcal/mol, log
A = 14.54.
1
Figure 1 Plot of log10(k, s 1) vs. inverse temperature, K
,
for the total isomerization of 1,1-dimethylcyclopropane to
methylbutenes: this study ( ); data reported by Flowers and
Frey [2a] (1).
The Arrhenius parameters reported above for
DMCP isomerization are identical to those reported by

KINETICS OF THE THERMAL ISOMERIZATION OF 1,1-DIMETHYLCYCLOPROPANE
857
Flowers and Frey [2a], within experimental uncer-
tainties. Comparing rate constant values measured in
the two studies, at 455.2 C Flowers and Frey found
for 1,1,2-trimethylcyclopropane structural isomeriza-
tion is similar to that for MCP, while that for isomeriza-
tion of 1,1,2,2-tetramethylcyclopropane rises further to
a value almost identical to that of the isomerization of
unsubstituted CP.
4
1
k = 1.82 10
s
while at 453 C the present study
gave k = 1.9 10 4 s 1. Similarly at 463 C, the Flow-
4
1
ers and Frey value of k = 2.94 10
s
compares
4
favorably with our value of k = 3.21 10
s
1. This
CONCLUSIONS
excellentagreementofrateconstantsfromthetwostud-
ies at the lower temperatures has confirmed the accu-
racy of the previously reported rate constants, and the
extension of the study to the higher temperatures has
lowered the uncertainty in the Arrhenius parameters for
the overall isomerization of DMCP.
The kinetic parameters for the thermal isomerization
of 1,1-dimethylcyclopropane have been redeter-
mined over a much wider range of temperatures,
683–1132 K, than that previously reported. The act
of essentially reproducing the earlier measured rate
constants plus greatly extending the temperature range
covered has increased the confidence in the activation
parameters. Comparing the activation parameters
for the structural isomerizations of cyclopropane
(Ea = 65.0 kcal/mol, log10 A = 15.20), methylcyclo-
propane (Ea = 64.6 kcal/mol, log10 A = 15.37), and
now 1,1-dimethylcyclopropane (Ea = 61.8 kcal/mol,
log10 A = 15.04) confirms that the cleavage of the C C
bond in the cyclopropane ring requires less energy
as H atoms on one of the carbons rings are replaced
by methyl groups, consistent with expectations [7]. It
is suggested that this series (CP, MCP, and DMCP)
presents a useful test of the ability of computational
methods to correctly account for the effects of methyl
substituents on the transition state energies and
structures.
The fact that essentially identical activation param-
eters for DMCP isomerization are obtained from the
shock-tube data in this study, the data of Flowers and
Frey [2] and the data reduction connecting our high
and low temperature data is worthy of note, as it in-
dicates that the Arrhenius plot is essentially linear
over a range of eight orders of magnitude in the rate
constant.
The results from this investigation, the earlier stud-
ies by Flowers and Frey [2], and our work on the
isomerization of methylcyclopropane [1] clearly in-
dicate that the effect of replacing H atoms on the
cyclopropane ring by methyl groups is a trend to-
ward lower activation energies. Rossi [7] has shown
that the amount of energy required to break a C C
bond with a methyl substituent is less than that re-
quired to break a C C bond between unsubstituted
carbon atoms. Since the mechanism of cyclopropane
isomerization is believed to begin with the breaking
of a C C bond to form a diradical transition struc-
ture, a decrease in this energy requirement by alkyl
substituents should lead to a lowering of the activa-
tion energy for the structural isomerization of substi-
tuted cyclopropanes. With the addition of only one
methyl group in place of a H atom on the CP ring,
the activation energy for structural isomerization is
reduced from 65.0 kcal/mol for CP to 64.4 kcal/mol
for methylcyclopropane (MCP). Replacement of a sec-
ond H on the same C in the CP ring seems to have
an even stronger effect on the activation energy, as
the further reduction in going from MCP to DMCP
is over 2 kcal/mol. This might lead to an expectation
that further methyl-for-hydrogen substitution would
produce further lowering of the isomerization acti-
vation energy. However, this appears not to be the
case. Results from earlier studies of 1,1,2-trimethyl-,
and 1,1,2,2-tetramethylcyclopropane isomerization re-
actions [8a–d], combined with results of recently com-
pleted studies of the same reactions in our labora-
tory [8e–f], show a reversal in this trend upon addi-
tion of the third methyl group. The activation energy
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