Kinetics of the thermal isomerization of 1,1,2,2-tetramethylcyclopropane

Article abstract of DOI:10.1002/kin.20149

Reaction rates for the structural isomerization of 1,1,2,2- tetramethylcyclopropane to 2,4-dimethyl-2-pentene have been measured over a wide temperature range, 672-750 K in a static reactor and 1000-1120 K in a single-pulse shock tube. The combined data from the two temperature regions give Arrhenius parameters E_a = 64.7 (±0.5) kcal/mol and log ₁₀(A, s^-1) = 15.47 (±0.13). These values lie at the upper end of the ranges of E_a and log A values (62.2-64.7 kcal/mol and 14.82-15.55. respectively) obtained from three previous experimental studies, each of which covered a narrower temperature range. The previously noted trend toward lower E_d values for structural isomerization of methylcyclopropanes as methyl substitution increases extends only through the dimethylcyclopropanes (1,1- and 1,2-); E_a then appears to increase with further methyl substitution. In contrast, the pre-exponential factors for isomerization of cyclopropane and all of the methylcyclopropanes through tetramethylcyclopropane lie within ±0.3 of log₁₀(A,s ^-1) = 15.2 and show no particular trend with increasing substitution.

Full text of DOI:10.1002/kin.20149

Kinetics of the Thermal
Isomerization of 1,1,2,2-
Tetramethylcyclopropane
DAVID K. LEWIS,1 TIMOTHY GRAY,1 VLAD KATSVA,1 KYLE PARCELLA,1 JESSICA SCHLIER,1
BANSI L. KALRA,2 JANET CHO,2 DEBRA MISH2
1Department of Chemistry, Connecticut College, New London, CT 06320
2Department of Chemistry, Hollins University, Roanoke, VA 24020
Received 1 July 2003; revised 8 September 2005; accepted 21 September 2005
DOI 10.1002/kin.20149
Published online in Wiley InterScience (www.interscience.wiley.com).
ABSTRACT: Reaction rates for the structural isomerization of 1,1,2,2-tetramethylcyclopropane
to 2,4-dimethyl-2-pentene have been measured over a wide temperature range, 672–750 K in a
static reactor and 1000–1120 K in a single-pulse shock tube. The combined data from the two
temperature regions give Arrhenius parameters Ea = 64.7 ( 0.5) kcal/mol and log10(A, s−1) =
15.47 ( 0.13). These values lie at the upper end of the ranges of Ea and log A values (62.2–
64.7 kcal/mol and 14.82–15.55, respectively) obtained from three previous experimental studies,
each of which covered a narrower temperature range. The previously noted trend toward lower
Ea values for structural isomerization of methylcyclopropanes as methyl substitution increases
extends only through the dimethylcyclopropanes (1,1- and 1,2-); Ea then appears to increase
with further methyl substitution. In contrast, the pre-exponential factors for isomerization of
cyclopropane and all of the methylcyclopropanes through tetramethylcyclopropane lie within
0.3 of log10(A, s−1) = 15.2 and show no particular trend with increasing substitution. ꢀ 2006
C
Wiley Periodicals, Inc. Int J Chem Kinet 38: 483–488, 2006
action rates and activation parameters, coupled with
the relative simplicity and high symmetry of the cyclo-
propane ring, have made reactions of CP and its alkyl
derivatives convenient test cases for the development
of computational models which examine the energies
of transition states and the dynamics of intramolecular
motions in the approach to those transition states.
Previous kinetic studies have shown that as methyl
groups are substituted for H atoms on the cyclopropane
ring, activation energies for structural isomerization
decrease, at least through the series cyclopropane,
Ea = 65.0 kcal/mol [1]; methylcyclopropane (MCP)
64.4 kcal/mol [2]; 1,1-dimethylcyclopropane (di-
MCP), 61.8 kcal/mol [3]; and 1,2-dimethylcyclo-
propane, 61.2–62.3 kcal/mol [4]. This trend has been
attributed to a weakening of the C C bonds in the
highly strained cyclopropane ring, leading to a lower
INTRODUCTION
Experimental kinetic studies of structural and geomet-
ric isomerizations of cyclopropane (CP) and various
alkyl-substituted cyclopropanes have been carried out
by a number of research groups over the past half cen-
tury. The wealth of experimental data available on re-
Jessica Schlier is a visiting student from Wesleyan University,
Middletown, CT 06459.
Correspondence to: David K. Lewis; e-mail: david.lewis@
conncoll.edu; B. L. Kalra; e-mail: bkalra@hollins.edu.
Contract grant sponsor: NSF.
Contract grant numbers: CHE 9714356 and CHE 0213374.
Contract grant sponsor: Cottrell College Science grant of
Research Corporation.
Contract grant sponsor: Connecticut College.
2006 Wiley Periodicals, Inc.
c
ꢀ

484
LEWIS ET AL.
energy barrier for formation of a diradical intermediate.
An earlier study of 1,1,2-trimethylcyclopropane (tri-
MCP) isomerization gave a value of Ea, 61.1 kcal/mol
[5]; however, in our systematic re-examination of these
reactions, that isomerization has yielded a somewhat
higher Ea value, 63.7 kcal/mol [6]. This suggests that
factors other than just the strength of the C C bond
being broken become important as more hydrogen
atoms on the cyclopropane ring are replaced by methyl
groups. The added steric interactions may distort the
transition state or block some easy pathways to it.
Continuing this exploration of the effects of suc-
cessive methyl-for-hydrogen substitutions on the ki-
netics and energetics of cyclopropane isomerizations,
we have now looked at the next more highly substituted
member of the series, 1,1,2,2-tetramethylcyclopropane
(tetra-MCP). This should be an ideal molecule for
kinetic-mechanistic studies, both experimental and the-
oretical, because isomerization via the expected dirad-
ical intermediate should form only a single product,
2,4-dimethyl-2-pentene (2,4-DMP).
1077–1151 K. Under the extremely homogeneous con-
ditions in the shock tube, he found evidence of only one
channel for tetra-MCP depletion, the isomerization to
2,4-DMP; at rates given by Ea = 62.2 kcal/mol, log
A = 14.82. However, Tsang did note considerable in-
stability of the product at these temperatures and had
to correct for its loss in calculating rate constants for
the tetra-MCP isomerization [10].
Given the similarity in absolute rates reported in the
two experimental static reactor studies [7,8], and the
care with which all three previous experimental studies
appear to have been carried out [7,8,10], it is unlikely
that there are large errors in the reported experiment-
based Arrhenius parameters. Still, in each of those stud-
ies, rate constant corrections were necessary for the
appearance of side products in experiments that con-
sumedsubstantialfractionsofthereactant. Considering
the importance of cyclopropane isomerizations to the
development and verification of computational meth-
ods, activation parameters of the highest accuracy now
possible should be made available. That is the purpose
of this study.
There have been three previous reports of experi-
mental rate studies of tetra-MCP isomerization. Frey
and Marshall [7] performed a static reactor study over
the range 708–757 K and found the reaction to be ho-
mogeneous and unimolecular, with Ea = 64.4 kcal/
mol and log (A, s−1) = 15.83 (later adjusted slightly to
Ea = 64.7 kcal/mol, log A = 15.55) [8]. Believing the
work of Frey and Marshall basically sound but possibly
affected by a systematic error due to the small temper-
ature range covered (50◦C), Benson and O’Neal [9]
combined a calculated pre-exponential factor based on
a diradical transition state with the experimental rate
constants in the center of Frey and Marshall’s temper-
ature range and concluded that Ea = 59.7 kcal/mol,
log A = 14.4 best described the rate of this isomer-
ization, thus continuing the trend of lower Ea with in-
creasing methyl substitution reported for other methyl-
substituted cyclopropanes. At that time, no other alkyl-
cyclopropane isomerization showed such a large dis-
crepancy between measured [7] and predicted [9] Ar-
rhenius parameters.
Shortly thereafter, two other experimental studies
were carried out to resolve this discrepancy. Blumstein
et al. [8] repeated the work in a static reactor at
699–759 K, and reported Ea = 63.93 kcal/mol, log
A = 15.27, within experimental error of the findings
of Frey and Marshall [7]. However, they believed this
to be the result of two parallel channels for loss of
tetra-MCP, the expected isomerization to 2,4-DMP
(with Ea = 62.3 kcal/mol) plus a minor but signifi-
cant decomposition pathway via loss of methyl radi-
cal (with Ea = 77 kcal/mol). Tsang [10] studied tetra-
MCP isomerization in a single-pulse shock tube at
In the work described here, the isomerization of
tetra-MCP to 2,4-DMP was studied over 672–750 K in
three glass static reactor cells, and at 1000–1120 K in a
glass single pulse shock tube, using two alternate ref-
erence reactions for temperature determination. Com-
bining the two experimental methods, we were able to
cover a wide temperature range, 448◦ in this study. We
were also able to restrict the rate data we used to runs
in which extents of depletion of the reactant tetra-MCP
were relatively small (generally <25%), eliminating
the need to know whether any side products observed
were produced directly from the reactant or from sub-
sequent reactions of the primary isomerization product
2,4-DMP.
EXPERIMENTAL SECTION
Materials
Tetra-MCP(99.96%)1 wasobtainedfromtheAPIStan-
dard Reference Materials project at Carnegie Mellon
University. Either Matheson CP grade (99%) cyclo-
propane (CP) or Aldrich reagent grade (99%) cyclo-
hexene (CH) was added to each reactant mixture
as an internal thermometer. These reagents, in ap-
propriate ratios, were diluted with Matheson reagent
grade (99.9999%) argon to prepare reaction mixtures.
1Reagent purities listed here are as specified by the vendors from
whom the samples were obtained. GC analyses confirmed these
percentages.

KINETICS OF THE THERMAL ISOMERIZATION OF 1,1,2,2-TETRAMETHYLCYCLOPROPANE
485
Samples of 2,4-DMP (99.6%) and a variety of other
Kinetic Runs
reagents from ChemSampCo (formerly Wiley Organ-
ics, Inc.) were diluted with argon and used for the
identification of products and as calibration mixtures.
All reagents were degassed before use through mul-
tiple freeze–pump–thaw cycles, then distilled from
the liquid phase into a gas storage bulb leaving be-
hind any less volatile impurities. High purity grade
helium was used as the driver gas in the shock-tube
runs.
For the runs at 672–750 K carried out in the static reac-
tor, the reactor cells were filled at room temperature to
pressuresrangingfrom89to328Torr, theninsertedinto
the hot oven for times ranging from 45 to 150 min. The
heating at constant volume produced pressures (calcu-
lated from measured initial pressure and ꢀT ) ranging
from 200 to 800 Torr during reaction. The cells were
removed from the reactor and cooled rapidly to room
temperature, then product gas was introduced into the
GC directly from the cells. Tests with an enclosed ther-
mocouple showed that it took somewhat longer for the
cells to reach reaction temperature when inserted into
the oven than to cool below reaction temperature when
removed; this thermal lag was corrected for in calcu-
lating the rate constants in Table II. Once a cell and
its contents reached thermal equilibrium with the oven
core, movement of the thermocouple along the cell’s
wall and within the heated gas produced temperature
variations of less than a degree.
For the shock tube experiments at 1000–1120 K,
sample mixture pressures introduced into the sample
section of the shock tube ranged from 35 to 100 Torr.
The reaction mixtures were heated for 800 50 μs at
total reaction pressures of 2–3 bar (p again calculated
from measured initial pressure and ꢀT ). Reaction time
was determined by measuring the duration of the high
pressure plateau (about 700 μs) and adding 100 μs,
or 14%. That percentage corresponds to the additional
product expected to be formed during the finite cool-
ing process assuming (1) an initial cooling rate (from
recorded pressure traces) of 5 × 105 K/s, (2) a first-
order irreversible reaction with Ea = 65 kcal/mol, and
(3) small extents of conversion of reactant to product
during the 700 μs plateau. As extent of conversion in-
creases, more reactant is consumed before the cooling
wave so less remains to react and the cooling correction
decreases. Thepercentageofproductformedduringthe
cooling is only moderately dependent on activation en-
ergy; for example, it should increase from 14% to 18%
if Ea dropped from 65 to 45 kcal/mol. Since the reac-
tions chosen as reference reactions have rate constants
and activation energies similar to the subject reaction,
there should be no significant error introduced by treat-
ing the experiment as an ideal “square wave” thermal
pulse of 800 μs duration rather than integrating down
the cooling curve to calculate the correction for each
product.
Apparatus
The static reactor used in this study is a well-insulated
aluminum-block tube furnace into which glass reac-
tor cells are inserted and removed to initiate and ter-
minate the reaction. Three 100 cm3 cells were used
randomly in this study; they were all well seasoned
through many hundreds of hours of heating while filled
with a variety of hydrocarbon gases. The cells were
evacuated and filled on an oil- and mercury-free high-
vacuum line. A fourth glass reactor cell was used ini-
tially, but then sidelined because of its curious ability
to produce an unexpected competing product at low
temperatures—see Results and Discussion. A 2.54-cm
diameter single-pulse shock tube was used for the
1000–1120 K experiment; its operating characteristics
have been described previously [11]. Reactant and
product samples were analyzed on a Varian 1440-20
gas chromatograph with hydrogen flame ionization de-
tector. A 3-m column containing 20% polypropylene
glycol saturated with AgNO3 on 80–100 mesh
Chromosorb W was used at room temperature.
Sample Preparation
Table I lists reaction mixtures containing different per-
centages of tetra-MCP and either CP or CH in argon;
these were prepared in 1- or 2-L glass storage flasks
with greaseless stopcocks and thoroughly mixed be-
fore use.
Table I Sample Reaction Mixtures
Reactor
%tetra-MCP %CP (or CH∗)
Single-pulse shock tube
0.67
2.00
3.00
1.02
1.18
2.00
0.67
2.00
3.00
0.99∗
2.26
2.00
Postshock samples extracted for the GC analysis
were taken by expansion into an evacuated 25 cm3 bulb
attached to the shock tube end plate, immediately af-
ter the shock. This is about 3% of the volume of the
shock tube sample section; therefore, it was assumed
Static reactor

486
LEWIS ET AL.
and Ea = 66.6 kcal/mol, log (A, s−1) = 15.15 for CH
[10]. For ln[(CP)t/(CP)0], we used GC peak heights
of CP and its isomerization product propene in heated
samples, again corrected for differences in GC detec-
tor response: ln[(CP)/(CP + propene)]. Similarly, GC
responses to 1,3-butadiene and CH were used for tem-
perature calculations for the samples to which CH
had been added. This assumes that all losses of CP
or CH were accounted for through product propene
or 1,3-butadiene, respectively. We believe that this is
supported by the absence of other product peaks at-
tributable to CP or CH decomposition, other than the
ethene co-produced from CH.
Table II Reaction Temperatures, Times, and Rate
Constants Displayed in Fig. 1
Temp (K)
Time
k (s−1
)
685.9
689.9
697.0
694.1
672.5
674.4
712.0
749.7
741.2
718.1
740.8
729.7
730.7
723.3
705.8
711.8
1081
1120
1105
1091
1090
1006
1017
1087
1062
1015
1098
1023
1004
1000
120 min
90 min
90 min
120 min
90 min
120 min
90 min
45 min
60 min
90 min
60 min
8.83 × 10−6
1.21 × 10−5
1.50 × 10−5
1.28 × 10−5
4.67 × 10−6
5.41 × 10−6
3.41 × 10−5
3.65 × 10−4
1.64 × 10−4
4.01 × 10−5
1.23 × 10−4
8.25 × 10−5
8.27 × 10−5
7.90 × 10−5
2.11 × 10−5
3.32 × 10−5
2.77 × 102
7.55 × 102
5.15 × 101
4.03 × 102
3.96 × 102
3.62 × 101
3.75 × 101
2.92 × 102
1.53 × 102
3.95 × 101
2.14 × 102
4.79 × 101
2.95 × 102
2.82 × 101
60 min
60 min
60 min
60 min
RESULTS AND DISCUSSION
At temperatures below 1200 K, structural isomeriza-
tion of cyclopropanes is generally believed to occur
mainly via cleavage of a C C bond to form a 1,3-
diradical, followed by 1,2-hydrogen transfer to form
a product alkene. As expected from this mechanism,
2,4-DMP was the major product, and in most experi-
ments the only product, formed from tetra-MCP iso-
merization. Conditions that produced other detectable
products are described below.
60 min
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
8.0 × 10−4
s
s
s
s
s
s
s
s
s
s
s
s
s
s
that the sample taken for analysis (compressed more
than five-fold during the reaction) resided very close to
the end plate where reaction time was measured, while
reacting.
Table II lists the reaction temperatures, times, and
tetra-MCP isomerization rate constants for the 30 ki-
netic runs in the static reactor and the shock tube, and
the data are displayed in Fig. 1. Linear least squares
regression of the data gives log10 (A, s−1) = 15.47
( 0.13), Ea = 64.7 ( 0.5) kcal/mol. The error lim-
its represent one standard deviation; uncertainties at
the 95% confidence level are twice as large. These re-
sults lie at the top of the ranges of log A and Ea values
presented in the three earlier published experimental
studies [7,8,10], but within the probable error ranges
of those three studies. Figure 2 repeats the data presen-
tation of Fig. 1, with the data from the three previous
studies added for comparison.
Calculations
Rate constants for the thermal isomerization of tetra-
MCP were calculated from the extent of its conversion
to 2,4-DMP, as determined from the GC peak heights,
corrected for measured sensitivity differences, of the
hydrocarbons in the product samples. Rate constants
were calculated from the integrated rate expression
for an irreversible first-order reaction. Reaction tem-
peratures were determined from the extent of conver-
sion of CP to propene or of CH to 1,3-butadiene plus
ethene, using the well-established Arrhenius param-
eters for these irreversible first-order isomerizations:
Ea = 65.0 kcal/mol, log (A, s−1) = 15.2 for CP [1]
The isomerization of CP was used as the internal
thermometer in our earlier studies of other methylcy-
clopropane isomerizations [2,3,6], but we were con-
cerned that, in spite of the relatively high total pres-
sures and reactant loadings in the shock tube, the CP

KINETICS OF THE THERMAL ISOMERIZATION OF 1,1,2,2-TETRAMETHYLCYCLOPROPANE
487
The highest temperature shock tube experiment at
1120 K, and the four highest temperature static reactor
experiments at 735–750 K produced one additional hy-
drocarbon product—probably a C7 compound, but not
specifically identified—in amounts ranging from 5% to
17% of the primary product 2,4-DMP. However, sam-
ples of 2,4-DMP plus CP heated under equivalent con-
ditions did not produce this product, giving evidence
that it is produced directly from tetra-MCP and not
from subsequent reaction of product 2,4-DMP. Con-
sidering the small extents of conversion of the reactant,
the presence of this minor parallel reaction introduces
no significant error into calculated rate constants for
the tetra-MCP → 2,4-DMP isomerization.
Figure
1 Arrhenius plot for 1,1,2,2-tetramethylcycl-
opropane isomerization; ꢀ Runs with CH added; ꢁ runs with
CP added.
A curious phenomenon was observed during the
initial experiments carried out in the fourth 100-cm3
glass static reactor cell (designated cell #4): a previ-
ously unreported product of tetra-MCP isomerization,
2,3,3-trimethyl-1-butene (2,2,3-TMB) was produced at
temperatures below 750 K. The relative mole fraction
of this product, compared with that of 2,4-DMP, in-
creased with decreasing reaction temperature, and at
temperatures below 672 K (and on down to 564 K), it
replaced 2,4-DMP as the only detectable product. Ex-
periments in reactor cells #1, 2, and 3 that yielded the
rate data presented in Fig. 1 produced no detectable
2,2,3-TMB. Analysis of the rate constants for 2,2,3-
TMB production in cell #4 gave an activation energy
of approximately 20 kcal/mol, suggestive of a wall-
catalyzed process. A sample of 2,4-DMP heated in cell
#4 for 60 min at 697 K produced no detectable 2,2,3-
TMB, indicating that 2,2,3-TMB is produced directly
from tetra-MCP. Cell #4 continues to produce exclu-
sively 2,2,3-TMB from tetra-MCP at temperatures be-
low 670 K, more than 8 years after the phenomenon
was first observed.
Figure
2 Arrhenius plot for 1,1,2,2-tetramethylcycl-
opropane isomerization, comparing present study to previ-
ous reports; u Runs with CP added; ꢂ runs with CH added;
ꢀ data of Tsang [10]; ꢃ data of Blumstein et al. [8]; ꢀ data
of Frey and Marshall [7].
reaction rate might have been slowed by unimolecu-
lar falloff. In studies comparing rates of CP and MCP
or di-MCP isomerizations [2,3], the similarities of the
reactant and reference molecules (similar numbers of
active vibrations) should have caused a canceling effect
of any minor rate reductions due to low-pressure falloff
that may have occurred. But we were less certain that
would be the case when comparing isomerization rates
of molecules as different as CP (nine atoms) and tetra-
MCP (21 atoms). Thus, CH, a 16-atom molecule, was
chosen as an alternative reference standard in some of
the shock tube runs. If the four data points that used CH
as the reference were removed from Table II and Fig. 1,
the least squares data reduction would give activation
parameters that are larger by less than half the stated
error limits (one standard deviation). This increases our
confidence that pressure falloff did not significantly al-
ter the activation parameters yielded by this study.
Why 2,2,3-TMB is produced, and produced cleanly,
from just that one heated reactor cell in our labora-
tory has defied explanation. Cell #4 had been used,
and continues to be used, for hydrocarbon isomeriza-
tion/decomposition studies, and has not produced un-
expected products or behavior from any other reactant.
The only clue is that, in some rate studies that pre-
ceeded the study of tetra-MCP isomerization, Lewis
acids BCl3 and BBr3 were introduced into that cell
to examine their catalytic effect on rates of structural
and geometric isomerizations of many hydrocarbons,
including other alkyl-substituted cyclopropanes [12].
However, experiments including those Lewis acids had
also been carried out in two of the other three reactor
cells, and no 2,2,3-TMB has been detected in the prod-
ucts of experiments run in those cells.
Table II lists the activation parameters deter-
mined in our laboratory for structural isomerization

488
LEWIS ET AL.
Table III Activation Parameters for Total Structural Isomerization Reactions (to All Product Isomers) for
Cyclopropane and Four Methylcyclopropanes
Reactant
log10 (A, s−1
)
Ea (kcal/mol)
k700 K (s−1
)
k1100 K (s−1
)
Ea**
Ref.
CP
MCP
di-MCP
tri-MCP
tetra-MCP
15.20
15.37
15.04
15.28
15.47
65.0
64.4
61.8
63.7
64.7
0.8 × 10−5
1.8 × 10−5
5.6 × 10−5
2.5 × 10−5
1.9 × 10−5
1.9 × 102
3.8 × 102
5.8 × 102
4.2 × 102
4.1 × 102
65.0
63.8
62.3
63.4
63.8
[1]
[2]
[3]
[6]
This work
Rate constants at 700 and 1100 K are taken from the least squares reduction of each data set. For the explanation of Ea∗∗ see text.
of cyclopropane and four methylcyclopropanes. There
is a clear trend of decreasing activation energies with
increasing methyl substitution from CP through di-
MCP, then a reversal of that trend with further methyl-
for-hydrogen substitution. In comparison, the pre-
exponential factors show no particular trend; in fact
they are equivalent (95% confidence level) at 15.2
( 0.3). Actual rate constants, at 700 K and at 1100 K,
increase with methyl substitution from CP through di-
MCP then decrease with further methyl substitution, in
step with the trend in activation energies.
Given the statistical equivalence (within 2σ uncer-
tainty ranges) of the pre-exponential factors for to-
tal structural isomerization of cyclopropane and four
methylcyclopropanes, it is interesting to compare the
activation energies that are obtained from the experi-
mental rate data (using average k values at 700 K from
each study) if log A is taken to be 15.2 for each re-
action. Those values are included in Table III as Ea∗∗.
This comparison produces a more even decline of 1.2–
1.5 kcal/mol per methyl group added to CP from CP
through di-MCP, followed by a gradual rise in Ea with
further methyl substitution. We propose that this is the
best overall representation of the activation parameters
for CP and the family of methylcyclopropanes from
MCP through tetra-MCP.
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B.L.K. thanks Hollins University for partial support. We also
thank Steven Hughes, Kevin Wilkinson, and Sara Wilkinson
for their assistance with portions of this study.