Microkinetic modeling of cis-cyclooctene oxidation on heterogeneous Mn-tmtacn complexes

Article abstract of DOI:10.1016/j.jcat.2012.03.026

Experiments and microkinetic modeling were used to investigate the reaction mechanism of cis-cyclooctene oxidation with H₂O₂ on heterogeneous manganese 1,4,7-trimethyl-1,4,7-triazacyclononane (Mn-tmtacn) catalysts. A mechanism based on literature reports and model discrimination was identified that captured experimental data well, including data at reaction conditions that were not used for parameter estimation. H₂O ₂ activation on the heterogeneous catalytic complex was identified as the rate-determining step (RDS), and a simple analytical rate expression was derived using the RDS and the pseudo-steady-state approximation for all intermediates. Predicted reaction orders for cis-cyclooctene, water, H ₂O₂, catalyst, and diol and epoxide products are also consistent with experimental observations and can be rationalized according to the derived rate expression. In addition, the ratio of productive to unproductive H₂O₂ use is analyzed, and catalyst deactivation is found to be an important step in the reaction mechanism that is highly sensitive to temperature.

Full text of DOI:10.1016/j.jcat.2012.03.026

Journal of Catalysis 291 (2012) 17–25
Contents lists available at SciVerse ScienceDirect
Journal of Catalysis
journal homepage: www.elsevier.com/locate/jcat
Microkinetic modeling of cis-cyclooctene oxidation on heterogeneous
Mn–tmtacn complexes
⇑
Kathryn R. Bjorkman, Nicholas J. Schoenfeldt, Justin M. Notestein, Linda J. Broadbelt
Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Road, Technological Institute, Evanston, IL 60208, United States
a r t i c l e i n f o
a b s t r a c t
Article history:
Experiments and microkinetic modeling were used to investigate the reaction mechanism of cis-cyclooctene
oxidation with H2O2 on heterogeneous manganese 1,4,7-trimethyl-1,4,7-triazacyclononane (Mn–tmtacn)
catalysts. A mechanism based on literature reports and model discrimination was identified that captured
experimental data well, including data at reaction conditions that were not used for parameter estimation.
H2O2 activation on the heterogeneous catalytic complex was identified as the rate-determining step (RDS),
and a simple analytical rate expression was derived using the RDS and the pseudo-steady-state approxima-
tion for all intermediates. Predicted reaction orders for cis-cyclooctene, water, H2O2, catalyst, and diol and
epoxide products are also consistent with experimental observations and can be rationalized according to
the derived rate expression. In addition, the ratio of productive to unproductive H2O2 use is analyzed, and
catalyst deactivation is found to be an important step in the reaction mechanism that is highly sensitive
to temperature.
Received 27 January 2012
Revised 29 March 2012
Accepted 30 March 2012
Available online 16 May 2012
Keywords:
Heterogeneous
Mn–tmtacn
Hydrogen peroxide
Reaction mechanism
Microkinetic modeling
Oxidation
Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction
total turnovers compared to homogeneous species and control of
product selectivity to cis-cyclooctane diol (cis-diol) or cis-cyclooc-
Selective oxidation of alkenes to form epoxide and cis-diol prod-
ucts is an important industrial process [1] and has been shown to
proceed efficiently on manganese-based catalytic complexes [1–3].
Manganese 1,4,7-trimethyl-1,4,7-triazacyclononane (Mn–tmtacn)
complexes were first synthesized in the late 1980s [4] and were
originally best known for their use in detergents as active bleach-
ing catalysts [5]. The complexes are better known by synthetic
chemists for their effectiveness in catalyzing low-temperature oxi-
dation reactions such as alkene cis-dihydroxylation, epoxidation,
and other important industrial reactions [6]. In particular,
researchers have studied these complexes under homogeneous
conditions with additional co-catalysts, which greatly increase
the activity and selectivity to desired products while limiting cat-
alase activity [1,2,7,8].
Immobilized versions of homogeneous catalysts have also been
investigated on a wide variety of supports [9–11]. The use of heter-
ogeneous systems is motivated by higher catalytic activity, more
easily controlled product selectivity, ease in product separation
and recovery, and possible reuse of the catalyst compared to homo-
geneous counterparts [10,12,13]. Notestein et al. [11] have synthe-
sized heterogeneous Mn–tmtacn complexes that are self-assembled
on carboxylic acid-functionalized SiO2 (S-CA) (Fig. 1) and shown
them to selectively oxidize cis-cyclooctene with H2O2, improving
tane oxide (epoxide) products [11]. The carboxylic acid groups in
S-CA serve as a physical tether for the Mn–tmtacn complex to the
heterogeneous surface and as a co-catalyst for oxidation reactions.
However, the precise reaction mechanism is unknown. Detailed
understanding of the reaction mechanism for cis-cyclooctene oxida-
tion not only can inform us about the oxidation process, but also
may contribute to understanding of the heterogeneous catalytic
system as a whole.
Microkinetic modeling is a powerful computational analysis
tool used to examine complex catalytic reaction systems in terms
of elementary reactions and their interplay without assumptions
about the rate-determining step [14]. Microkinetic modeling has
been effective in elucidating reaction mechanisms for complex
reaction networks [14–19]. Possible reaction mechanisms are pro-
posed based on experimental measurements (e.g., spectroscopic
analysis of kinetic data) and theory (e.g., quantum mechanical
studies) and tested against experimental data to further develop
and refine the model. Analysis of the modeling results contributes
to additional insight into the reaction mechanism, such as predict-
ing data outside the experimental ranges that were studied, iden-
tifying rate-determining step(s), predicting reaction orders, and
determining important steps in the mechanism for future catalyst
development and optimization of the reaction conditions to tune
product selectivity.
In this work, we used experimental data and microkinetic mod-
eling to propose a reaction mechanism for cis-cyclooctene oxidation
on heterogeneous Mn–tmtacn catalytic complexes. The resulting
⇑
Corresponding author.
E-mail address: broadbelt@northwestern.edu (L.J. Broadbelt).
0021-9517/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.jcat.2012.03.026

18
K.R. Bjorkman et al. / Journal of Catalysis 291 (2012) 17–25
Fig. 1. Schematic of heterogeneous Mn–tmtacn complex, A, formed by the combination of the homogeneous complex, 1, and S-CA, 2 [11].
Table 1
Reaction conditions of numbered individual experiments. Experiments used for optimization of rate parameters (six in total) are in bold. Note that some experiments are listed
more than once for completeness because they were used in the determination of reaction orders for multiple species. Also, Experiments 22 and 23 were replicates of the same
conditions.
Description
Exp.
#
Temp.
(°C)
Vol.
(mL)
Catalyst (1)
mol)
[cis-Cyc]0
(M)
[H2O2]0
(M)
[H2O]0
(M)
[Epoxide]0
(M)
[cis-Diol]0
(M)
Mass balance
(%)
(
l
Varied temperature experiments
1
2
3
4
ꢀ10
0
25
50
45.6
45.6
45.6
45.6
6.8
0.16
0.17
0.16
0.17
0.60
0.60
0.60
0.56
2.7
2.7
2.7
2.5
0
0
0
0
0
0
0
0
97.3
94.8
96.5
86.9
6.8
6.8
6.8
Catalyst reaction order
experiments
5
0
45.6
0.9
0.17
0.56
2.5
0
0
81.1
6
7
8
9
10
11
0
0
0
0
0
0
45.6
45.6
45.6
45.6
45.6
45.6
2.3
4.6
6.8
9.1
16.5
24.2
0.17
0.17
0.16
0.17
0.17
0.17
0.56
0.56
0.56
0.56
0.56
0.56
2.5
2.5
2.5
2.5
2.5
2.5
0
0
0
0
0
0
0
0
0
0
0
0
88.3
94.0
88.4
96.7
95.1
92.4
cis-Cyclooctene reaction order
12
0
45.6
6.8
0.04
0.56
2.5
0
0
92.9
experiments
13
14
8
15
16
0
0
0
0
0
45.6
45.6
45.6
45.6
45.6
6.8
6.8
6.8
6.8
6.8
0.08
0.13
0.16
0.21
0.34
0.56
0.56
0.56
0.56
0.56
2.5
2.5
2.5
2.5
2.5
0
0
0
0
0
0
0
0
0
0
90.0
92.2
88.4
91.3
86.9
H2O2 reaction order experiments
H2O reaction order experiments
17
18
19
20
21
0
0
0
0
0
47.5
47.5
47.5
47.5
47.5
6.8
6.8
6.8
6.8
6.8
0.16
0.16
0.16
0.16
0.16
0.10
0.21
0.31
0.52
0.93
3.7
3.8
3.8
3.9
4.1
0
0
0
0
0
0
0
0
0
0
91.4
80.6
89.2
89.7
92.4
22
23
24
25
26
27
0
0
0
0
0
0
50.0
50.0
50.0
50.0
50.0
50.0
6.8
6.8
6.8
6.8
6.8
6.8
0.15
0.15
0.15
0.15
0.15
0.15
0.51
0.51
0.51
0.51
0.51
0.51
2.2
2.2
3.4
4.5
5.6
0
0
0
0
0
0
0
0
0
0
0
0
93.9
91.7
94.6
91.0
91.7
85.3
10.0
Epoxide reaction order
experiments
22
0
50.0
6.8
0.15
0.51
2.2
0
0
93.9
23
28
29
30
31
32
33
0
0
0
0
0
0
0
50.0
50.0
50.0
50.0
50.0
50.0
50.0
6.8
6.8
6.8
6.8
6.8
6.8
6.8
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.51
0.51
0.51
0.51
0.51
0.51
0.51
2.2
2.2
2.2
2.2
2.2
2.2
2.2
0
0
0
0
0
0
0
0
91.7
91.0
93.8
87.4
89.3
92.8
86.9
0.009
0.018
0.024
0.037
0.042
0.062
cis-Diol reaction order experiments 22
0
0
0
0
0
0
0
0
50.0
50.0
50.0
50.0
50.0
50.0
50.0
50.0
6.8
6.8
6.8
6.8
6.8
6.8
6.8
6.8
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.51
0.51
0.51
0.51
0.51
0.51
0.51
0.51
2.2
2.2
2.2
2.2
2.2
2.2
2.2
2.2
0
0
0
0
0
0
0
0
0
0
93.9
91.7
94.2
88.3
92.8
92.7
93.6
109.1
23
34
35
36
37
38
39
0.013
0.014
0.020
0.028
0.046
0.080
Titrated H2O2 experiments
40
41
42
0
25
0
91.2
91.2
91.2
6.8
6.8
6.8
0.17
0.17
0
0.54
0.39
0.67
2.4
2.5
2.4
0
0
0
0
0
0
103.2
105.8
–

K.R. Bjorkman et al. / Journal of Catalysis 291 (2012) 17–25
19
Fig. 2. Proposed catalytic cycle for cis-cyclooctene oxidation on heterogeneous Mn–tmtacn catalysts.
microkinetic model successfully predicts overall experimental
trends and reaction orders and allows the rate-determining step
of the reaction mechanism to be identified. Microkinetic modeling
was also used to compare the rates of competing reactions and iden-
tify the degree of catalyst deactivation as a function of reaction con-
ditions, providing insight into a quantity that was not accessible
experimentally.
co-catalytic support prior to substrate addition [11]. Following
the pre-treatment period, freshly distilled cis-cyclooctene [25]
was added, and small aliquots of the reaction mixture were re-
moved periodically for analysis. During each experiment, the total
amount removed for analysis was less than 10% of the initial reac-
tion solution and a similar amount of the suspended catalyst, min-
imizing any changes in catalyst concentration throughout the
experiment. Prior to gas chromatography (GC) analysis, the ali-
quots were filtered through Whatman GF/F syringe filters and were
subjected to small amounts of Ag powder to remove unreacted
H2O2 prior to GC injection, thus minimizing the formation of
over-oxidation products external to the reaction vessel. Leaching
tests on related systems confirmed that the solution above the sol-
ids contained no catalytically active species [11]. Ag powder was
found to be unreactive with reaction products during control reac-
tions. All experiments were performed at atmospheric pressure
and were open to air; the oxygen concentrations in solution were
assumed to follow standard solubility in water under like condi-
tions [26,27].
Reaction rate order data were obtained by holding the initial
concentrations of all but one component constant, while varying
the initial concentration of the component of interest; Table 1 con-
tains initial reaction conditions for each experiment, including
baseline experiments for reactant and product kinetic experi-
ments. Additional reactions with similar initial concentrations
were carried out at ꢀ10 °C, 25 °C, and 50 °C. The average final mass
balance (produced cis-diol + epoxide per cis-cyclooctene con-
sumed) calculated from experimental data was 92%, with a range
of 80% and 110% for all reactions; values for specific experiments
are also included in Table 1. Concentrations were chosen such that
all the reactants and products are soluble at all conversions at
ꢀ10 °C and higher. Freezing is avoided at ꢀ10 °C because MeCN
(freezing point of ꢀ45 °C) is the bulk of the solution. Reactions with
varied reaction temperature were carried out at least twice; error
bars represent standard deviation between the trials at each time
point. Select experiments also included time-dependent H2O2 con-
centration measurements, which were determined via iodometric
titration of small aliquots of reaction solution using 0.1 M Na2S2O3.
Additional information about the experimental setup can be found
in a recent publication by some of the authors [24].
2. Methods
2.1. Experimental details
1,4,7-Trimethyl-1,4,7-triazacyclononane (tmtacn) is available
commercially and can be prepared according to the literature
methods [20,21]. Manganese tmtacn dimeric complex, 1 (Fig. 1),
was synthesized upon slow addition of a freshly prepared solution
of 1:1 H2O2(1.5 M)/NaOH(1.0 M) to a 0–2 °C solution containing
equimolar amounts of MnCl2ꢁ4H2O and tmtacn and 1.5 eq KPF6
in acetonitrile, followed by filtration and crystallization from
MeCN/EtOH solutions [20–22]. Carboxylic acid-modified SiO2 (S-
CA) (2 in Fig. 1) was synthesized by refluxing a desired quantity
of SiO2, which had previously been dried at 120 °C under vacuum
for 12–15 h, with 2-(carbomethoxy)ethyltrimethoxysilane (Gelest)
in pyridine for 18–24 h followed by refluxing in 1.0 M HCl to con-
vert the supported ester functionality into surface carboxylic acids
[23]. The modified SiO2 supports were Soxhlet extracted with ben-
zene for 18–24 h and vacuum dried prior to and following the acid
de-protection step. Smaller S-CA particle sizes were used for reac-
tions carried out at higher temperatures to minimize any possible
mass transport effects [24].
Batch kinetic studies were carried out at a constant reaction
temperature (ꢀ10, 0, 25, or 50 °C) using a cold-plate stirrer
(Thermoelectrics Unlimited, Inc.) or a hot-plate stirrer with a fab-
ricated aluminum block (IKA). The reaction flask containing HPLC
grade MeCN, 1, S-CA, and o-dichlorobenzene (as internal standard)
was equilibrated to the desired temperature with magnetic stir-
ring. 30 wt.% aqueous H2O2 was then added, and the mixture was
allowed to pre-treat with stirring for 40 min. The H2O2 pre-treat-
ment period was employed to immobilize the catalyst onto the

20
K.R. Bjorkman et al. / Journal of Catalysis 291 (2012) 17–25
Table 2
Optimized rate parameters for microkinetic model. Parameters in bold were optimized, while all others were fixed based on statistical mechanical estimates.
Reaction
Pre-exponential factor, A
Activation Energy, Ea (kJ/mol)
Rate constant, k, at 0 °C
Keq = kf/kr
1, forward
1, reverse
2, forward
2, reverse
3, forward
3, reverse
4, forward
4, reverse
5, forward
5, reverse
6, forward
7, forward
7, reverse
8, forward
1.0 ꢂ 107 Mꢀ1 sꢀ1
10.5
66.9
42.7
81.6
49.0
64.9
51.9
59.4
50.2
0.8
9.9 ꢂ 104 Mꢀ1 sꢀ1
2.0 ꢂ 1017 sꢀ1
3.3 ꢂ 104 sꢀ1
3.0 ꢂ 100 Mꢀ1
5.1 ꢂ 108
5.0 ꢂ 107 Mꢀ1 sꢀ1
3.0 ꢂ 106 Mꢀ1 sꢀ1
1.0 ꢂ 1010 Mꢀ1 sꢀ1
1.0 ꢂ 109 sꢀ1
3.7 ꢂ 10ꢀ1 Mꢀ1 sꢀ1
ꢀ1
7.2 ꢂ 10ꢀ10 Mꢀ1
s
4.5 ꢂ 100 Mꢀ1 sꢀ1
4.0 ꢂ 10ꢀ4 sꢀ1
1.1 ꢂ 104 Mꢀ1
1.0 ꢂ 1010 sꢀ1
1.1 ꢂ 100 sꢀ1
1.7 ꢂ 1012 Mꢀ1 sꢀ1
1.0 ꢂ 109 sꢀ1
7.2 ꢂ 100 Mꢀ1 sꢀ1
2.6 ꢂ 10ꢀ1 sꢀ1
1.5 ꢂ 10ꢀ1
4.4 ꢂ 10ꢀ2
M
M
8.3 ꢂ 100 Mꢀ1 ꢀ1
s
s
5.7 ꢂ 100 Mꢀ1 sꢀ1
1.9 ꢂ 10ꢀ2 Mꢀ1 sꢀ1
2.9 ꢂ 10ꢀ4 Mꢀ1 sꢀ1
5.0 ꢂ 108 Mꢀ1 ꢀ1
54.4
61.9
292.9
25.1
2.0 ꢂ 108 Mꢀ1 ꢀ1
s
s
5.0 ꢂ 107 Mꢀ1 ꢀ1
4.2 ꢂ 10ꢀ49 Mꢀ1
s
6.9 ꢂ 1044
ꢀ1
1.0 ꢂ 105 Mꢀ1 sꢀ1
1.4 ꢂ 100 Mꢀ1 sꢀ1
bounds (up to 125 kJ molꢀ1) that were refined based on parameter
estimation and sensitivity analysis. The parameter space was
further constrained by the use of overall reaction free energies
for epoxide and cis-diol formation from cis-cyclooctene,
2.2. Mechanism selection
A potential reaction mechanism for the microkinetic model
(Fig. 2) was proposed based on a similar reaction mechanism pub-
lished by de Boer et al. [3] to describe alkene oxidation by H2O2
with dinuclear Mn bis(carboxylato)-bridged complexes, a homoge-
neous analog to the present heterogeneous system. The final reac-
tion mechanism focuses on a single catalytically active species that
activates H2O2 to produce both cis-diol and epoxide products and is
supported by kinetic data analysis as well as 18O isotopic labeling
studies. In Step 1, the heterogeneous Mn–tmtacn complex A com-
bines with H2O, opening the oxo bridge between the Mn atoms to
form B. H2O2 reacts with B to form the activated complex C (Step
2). This complex then is able to combine with cis-cyclooctene to
form a loosely alkene-coordinated intermediate D in Step 3. This
intermediate proceeds to form epoxide and cis-diol products via
the alkene-coordinated intermediate D (Steps 4 and 5). An addi-
tional H2O2 decomposition step involving complex C is incorpo-
rated into the core catalytic cycle (Step 6), as well as a catalyst
deactivation step leading to inactive catalyst (Step 7). H2O2 is also
decomposed via the inactive catalyst species (Step 8). All reactions
are allowed to be reversible except for H2O2 decomposition steps
(Steps 6 and 8), as the reverse of these reactions would involve
an unfavorable trimolecular reaction. The addition of these deacti-
vation steps to the core mechanism is motivated by experimental
observations of a marked decrease in turnover frequency over time
in early oxidation experiments [11]. The particular form of the
deactivation step was selected from several different candidates
that were tested against experimental data through model
discrimination.
D
Gf,epoxide = ꢀ62.26 kJ molꢀ1
,
and
D
Gf,cis-diol = ꢀ61.88 kJ molꢀ1
,
which were calculated using a group contribution method [29].
Both A and Ea values were initially optimized with weighted least
squares regression using a hybrid scheme with a genetic algorithm
2.3. Microkinetic modeling details
Microkinetic modeling was carried out by coupling the postu-
lated reaction mechanism with reactor design equations resulting
in a set of stiff differential and algebraic equations, which was
solved using DASSL [28]. Each reaction in the microkinetic model
was assumed to follow mass action kinetics with rate laws based
on elementary steps and rate coefficients calculated using the
Arrhenius equation as described in Eq. (1):
a=RT
k ¼ AeꢀE
ð1Þ
where A is the pre-exponential factor, Ea is the activation energy, R
is the ideal gas constant, and T is the temperature. Reaction rate
constants for individual elementary steps were unavailable for the
heterogeneous reaction system or even the homogeneous analog
so reasonable ranges of A values were selected based on statistical
mechanical estimates [14]. Ea values were initially given wide
Fig. 3. Parity plots for experimental data versus model observations that are (a)
fitted and (b) predicted (see Table 1).

K.R. Bjorkman et al. / Journal of Catalysis 291 (2012) 17–25
21
Fig. 4. Model predictions (lines) compared to experimental observations (points) for varying initial concentrations of cis-cyclooctene and H2O2. The experiments shown are
(a) #13, (b) #8, (c) #16, (d) #17, (e) #19, and (f) #21 (Table 1).
(GA) [30] as a stochastic global optimizer and a gradient-based local
optimizer (GREG) [31]. The weighting function used was the
following:
data (experiments in bold listed in Table 1) was used to optimize
rate parameters, amounting to 234 total experimental data points.
Five different runs varied according to the initial populations were
conducted with one cycle of parameter optimization, which in-
cluded five iterations of the GA-GREG scheme. For the GA part of
the optimization, a population of 400 individuals (i.e., sets of rate
parameters) was randomly selected within specified bounds and al-
lowed to intermingle with other individuals according to estab-
lished probabilities of natural selection [19,30]. The overall
probability of crossover between individuals was 0.8, and the indi-
vidual arithmetic-, heuristic-, and simple-crossover probabilities
were set to 0.1, 0.95, and 1.0, respectively. The overall probability
1
wi ¼
ð2Þ
ri ꢁ yi
where i represents a particular experimental observation, wi is the
weighting factor, ri is the standard deviation, and yi is the experi-
mentally observed value. Calculated standard deviations were used
for experimental data where available; for all others, a standard
deviation of 10% was used. A subset of the available experimental

22
K.R. Bjorkman et al. / Journal of Catalysis 291 (2012) 17–25
Table 3
Comparison of reaction orders calculated from initial rates of reaction based on cis-
cyclooctene consumption.
Reaction orders
Model
Experimental
Catalyst (1)
cis-Cyclooctene
H2O2
H2O
Epoxide
cis-Diol
0.93
0.25
0.81
0.04
0.07
0.09
0.82
0.23
0.58
0.00
0.08
0.15
other products for which no single species was in high enough con-
centration to be quantified by GC, and which are therefore not
present in the microkinetic model. Table 2 contains the optimized
rate parameters for the microkinetic model, with individual pre-
exponential factors, activation energy barriers, rate constants cal-
culated at 0 °C, and equilibrium constants for each reversible step
of the reaction.
The performance of the microkinetic model is even better dem-
onstrated by showing how well it predicts temporal experimental
trends, especially as the rate of product formation decreases over
time. Selected experimental results are shown in Fig. 4 for different
initial concentrations of cis-cyclooctene and H2O2 that are pure
predictions. Notably, the microkinetic model is able to capture
the curvature of these plots as the time progresses, lending further
support to the catalyst deactivation step proposed in addition to
the core catalytic cycle from literature. These results illustrate
the predictive power of microkinetic modeling for various reaction
conditions, including additional reaction temperatures. The identi-
fication of the A and Ea components of the rate coefficients allows
us to predict experimental reaction profiles at room temperature
(Fig. 5).
Fig. 5. cis-Cyclooctene oxidation at 25 °C. Model observations are predicted based
on microkinetic model and final optimized rate parameters.
to undergo mutation was set to 0.2, and the individual probabilities
of boundary-, Gaussian-, non-uniform-, and uniform mutations
were set to 0.2, 0.8, 0.9, and 1.0, respectively. Elitism was applied
by preserving the top five individuals for the next generation of
individuals. Once an optimal set of rate parameters based on the
lowest sum of squares (SSQs) was established with the initial cycle
of parameter optimization, the resulting parameters were re-opti-
mized again for a total of ten cycles with varied parameter bounds
up to 50% to further reduce the SSQ. This procedure was performed
a total of five times, resulting in a set of optimized rate parameters.
Sensitivity analysis revealed the nine parameters to which the
model was most sensitive. All other parameters were fixed based
on statistical mechanical estimates, and finally, nine activation
energies were optimized to obtain the final set of parameters
reported in Table 2.
Given the ability of the microkinetic model to both fit and pre-
dict the experimental data well, the model was further analyzed
with two methods to identify the rate-determining step of the
cis-cyclooctene reaction mechanism. In the first method, the ratio
of the net rate to the forward rate of reaction was calculated; if
the value is close to zero, the step is quasi-equilibrated, and if
the value is close to one, the step is considered to be rate-deter-
mining. The second method calculates the degree of rate control
Xrc,i for each step i, defined by Eq. (3):
3. Results and discussion
The overall performance of the microkinetic model is summa-
rized in the parity plots in Fig. 3 which compare the experimental
observations with both model fits (Fig. 3a) and model predictions
(Fig. 3b). The results indicate that the microkinetic model both
accurately captures the data against which it was optimized and
successfully predicts observations for other initial conditions. The
trend of overpredicting reactant (cis-cyclooctene) and under-pre-
dicting product (epoxide and cis-diol) concentrations is a conse-
quence of some oxidation of reactants and products to several
ꢀ
ꢁꢀ
ꢁ
ki
R
dR
dki
Xrc;i
¼
ð3Þ
where ki is the rate constant for step i, R is the overall rate of reac-
tion, and the partial derivative (dR/dki) is taken while holding the
equilibrium constant for step i and all other rate parameters con-
stant [32]. The degree of rate control is then compared for each
reaction; if the value is above the proposed limit of 0.95, the step
is rate-determining. For both methods, the activation of complex
B by H2O2 (Step 2 in Fig. 2) was identified as the rate-determining
step of the reaction mechanism.
Another basis of comparison of the microkinetic model and the
experimental data is the overall reaction orders with respect to dif-
ferent species based on initial rates. The microkinetic model was run
at a series of different initial concentrations of the different compo-
nents at 0 °C, and initial rates were calculated based on average cis-
cyclooctene consumption at times less than 30 min. This time frame
was selected based on linearity of the concentration versus time
plots up to this point and to keep consistent between experiments;
the average R2 values of the initial rate regressions were greater
than 0.99 and 0.87 for the model predictions and experimental data,
respectively. The microkinetic model is able to predict reaction or-
ders consistent with those obtained by experimental values (Table
3). cis-Cyclooctene oxidation on the heterogeneous Mn–tmtacn
Fig. 6. Productive vs. unproductive use of H2O2 in cis-cyclooctene oxidation for
various temperatures as a function of time, calculated by taking the ratio of the
rates of H2O2 activation of the Mn–tmtacn complex (Step 2) and H2O2 deactivation
reactions (Steps 6 and 8). The ratio is graphed in log scale with RH2O2 utilized = 1
delineated to highlight the times at which unproductive use of H2O2 becomes
dominant at each temperature.

K.R. Bjorkman et al. / Journal of Catalysis 291 (2012) 17–25
23
Fig. 7. Prediction of formation of deactivated catalyst with respect to time at various (a) initial catalyst amounts (Experiments #5–11), (b) initial cis-cyclooctene
concentrations (Experiments #8 and 12–16), (c) initial H2O2 concentrations (Experiments #17–21), and (d) temperatures (Experiments #1–4). The fraction of deactivated
catalyst refers to the proportion of catalyst that has been deactivated compared to the initial amount added.
complex is found to be nearly first order with respect to the catalyst,
which is to be expected based on the topology of the mechanism.
cis-Cyclooctene oxidation was 0.25 order in cis-cyclooctene, 0.81 or-
der in H2O2, and zero order in epoxide and cis-diol products, as well
as water. Note that the orders with respect to cis-cyclooctene and
H2O2 are fractional. While fractional orders can be rationalized by
denominator. This expression also lends further support to the over-
all mechanism, as the balance of terms deriving from the various
intermediates (and therefore the number and complexity of inter-
mediates) is necessary to explain the complex species orders pres-
ent in this catalytic system.
k2;f k3;f ðk4;f þ k5;f Þ½H2O2ꢃ½H2Oꢃ½cycloocteneꢃ
ðk2;f k3;f ½H2O2ꢃ½H2Oꢃ½cycloocteneꢃ þ k1;f k3;f ðk4;f þ k5;f Þ½H2Oꢃ½cycloocteneꢃ þ ðk3;r þ k4;f þ k5;f Þðk6;f þ k2;f Þ½H2O2ꢃ½H2OꢃÞ
r ¼
ð4Þ
analytical rate expressions derived based on Langmuir–Hinshel-
wood–Hougen–Watson or pseudo-steady-state approximations,
these analyses are not able to easily handle the branched catalytic
cycle here, which includes a kinetically controlled deactivation step.
However, by neglecting catalyst deactivation at times less than
30 min, the core catalytic cycle (Steps 1–6 in Fig. 2) can be treated,
assuming the RDS and applying the pseudo-steady-state approxi-
mation for all intermediates to derive an analytical rate expression.
The full expression contains 29 terms and is shown in Appendix A.
On the basis of the rate parameters and ranges of concentrations,
terms that can be safely neglected at 0 °C were identified, and a sim-
pler expression in Eq. (4) was obtained. From this expression, the
zero-order dependence in water can be easily observed, as well as
the fractional order dependence in cis-cyclooctene and H2O2,
which results from a balance between terms in the numerator and
The next analysis carried out using the microkinetic model was
to quantify the balance between productive and unproductive use
of H2O2 as an oxidant. This was done by taking the ratio of reaction
rates (Eq. (5)):
r2;f ꢀ r2;r
RH
¼
ð5Þ
2O2 utilized
r6;f þ r8;f
where r2,f and r2,r are the forward and reverse reaction rates of H2O2
activation of complex B (Step 2), r6,f is the forward reaction rate of
H2O2 decomposition to H2O and O2, and r8,f is the forward reaction rate
of H2O2 decomposition by the inactivated catalyst (Step 8). This ratio
decreases with respect to time under all conditions and is insensitive
to initial concentrations of various species at 0 °C, but it exhibits a
strong dependence on temperature. The microkinetic model results
indicate that productive use of H2O2 is favored initially for lower

24
K.R. Bjorkman et al. / Journal of Catalysis 291 (2012) 17–25
deactivation, but at much lower rates. While increased temperature
will also necessarily increase the rate of cis-cyclooctene oxidation,
the result of this analysis indicates that the balance between oxida-
tion and catalyst deactivation should be carefully considered when
designing reaction conditions for further experimentation. We can
also quantify the importance of the catalyst deactivation step (Step
7 in Fig. 2) by performing sensitivity analysis related to the rate
coefficient, k7. Fig. 8 contains model predictions for cis-cyclooctene
conversion after increasing and decreasing k7 by a factor of two. If
one could modify the catalyst or support to reduce k7 by half, the
conversion would be increased from 0.43 to 0.60 at 0 °C and 0.13
to 0.23 at 50 °C; this indicates that reducing deactivation by a factor
of two for this catalyst has the potential to increase overall conver-
sion by 50–100% depending on operating temperature.
Fig. 8. cis-Cyclooctene conversion at 0 °C and 50 °C with experimental data
(points), model predictions with original k7 rate coefficient (solid lines), and model
predictions with k7 increased and decreased by a factor of two (shaded areas
bordered by dashed lines).
4. Conclusions
Microkinetic modeling was used in conjunction with experimental
observations to elucidate a serviceable reaction mechanism for cis-
cyclooctene oxidation with H2O2 on heterogeneous Mn–tmtacn cata-
lysts. The microkinetic model captures experimental data well and
successfully predicts experimental observations at reaction conditions
other than those that were used for parameter estimation. The rate-
determining step was found to be H2O2 activation by the heteroge-
neous catalytic complex, and a simple rate expression was derived,
assuming this RDS and applying the pseudo-steady-state approxima-
tion to all intermediates. The analytical rate expression is only applica-
ble at short times when the catalyst has not deactivated to a large
extent, but it provides a useful tool to rationalize the experimental
reaction orders. Microkinetic modeling results predicted reaction or-
ders consistent with experimental observations, and additional infor-
mation about competing reactions to consume H2O2 was gleaned,
revealing that productive use of H2O2 decreased with increasing tem-
perature. Deactivation of the catalyst was found to be a crucial part of
the reaction mechanism and sensitive to temperature, and the micr-
okinetic model allowed the fraction of deactivated catalyst as a func-
tion of various reaction conditions to be predicted.
Fig. A.1. Comparison of rates at 0 °C (Experiment 2) for analytical rate expressions
compared to the microkinetic model. The difference between the microkinetic
model and complete PSSA expression at longer times is a result of increasing
catalyst deactivation, which is not included in the idealized PSSA expression.
temperatures, but the ratio soon shifts to quantities less than one as the
reaction progresses (Fig. 6).
Acknowledgments
Finally, the microkinetic model was used to quantify the deacti-
vated catalyst as a function of time, temperature, and initial con-
centration of selected components (Fig. 7). This species was
unable to be isolated and characterized, but is hypothesized to be
small crystallites of MnO2 [24], which has been observed to effec-
tively decompose H2O2 under these conditions. While the initial
amount of catalyst had little effect on the proportion of deactivated
catalyst formed over time (Fig. 7a), the deactivation process was
slightly sensitive to cis-cyclooctene and H2O2 (Fig. 7b and c)
and very sensitive to temperature (Fig. 7d). The catalyst is com-
pletely deactivated after 20 min at 50 °C, compared to 60 min at
25 °C. Reactions carried out at 0 °C and ꢀ10 °C also exhibit catalyst
The authors would like to thank The Dow Chemical Company
and The Dow Methane Challenge for financial support, and Andrew
Korinda for useful discussions.
Appendix A. Analytical rate expression
The complete analytical rate expression derived from the RDS
and applying the pseudo-steady-state approximation to all inter-
mediates is listed in Eq. (A.1),
where
2
k2;f ½H2O2ꢃðk1;f k2;rkA½H2Oꢃ þk1;f k3;f kD½H2Oꢃ½cycloocteneꢃþk1;f k6;f kA½H2O2ꢃ½H2Oꢃþk2;rk5;rkE½H2Oꢃ½diolꢃþk5;rk6;f kE½H2O2ꢃ½diolꢃþk3;f k4;f k5;r½cycloocteneꢃ½diolꢃÞ
r ¼
2
ðk1;f k2;rk4;r½H2Oꢃ ½epoxideꢃþk1;f k2;f k3;f ½H2O2ꢃ½H2Oꢃ½cycloocteneꢃþk1;f k4;rk6;f ½H2O2ꢃ½H2Oꢃ½epoxideꢃ
þk1;f k3;f k4;r½H2Oꢃ½cycloocteneꢃ½epoxideꢃþk2;rk4;rk5;r½H2Oꢃ½diolꢃ½epoxideꢃ
2
þk4;rk5;f k5;r½H2O2ꢃ½diolꢃ½epoxideꢃþk2;f k3;f k5;r½H2O2ꢃ½cycloocteneꢃ½diolꢃþk1;f k2;rkA½H2Oꢃ
þk3;f k4;rk5;r½cycloocteneꢃ½epoxideꢃ½diolꢃþk1;f kAðk2;f þk6;f Þ½H2Oꢃ½H2O2ꢃþk2;rk5;rkB½H2Oꢃ½diolꢃ
þk1;f k3;f kD½H2Oꢃ½cycloocteneꢃþk4;rðk1;f k3;r þk2;rk5;f Þ½H2Oꢃ½epoxideꢃþk4;rk5;f k6;f ½H2O2ꢃ½epoxideꢃ
þk2;f k3;f k5;f ½H2O2ꢃ½cycloocteneꢃþk3;rk4;rk5;r½epoxideꢃ½diolꢃþk5;rðk2;f kE þk6;f kBÞ½H2O2ꢃ½diolꢃ
þk3;f k4;rk5;f ½cycloocteneꢃ½epoxideꢃþk3;f k5;rkC ½cycloocteneꢃ½diolꢃþk1;rk2;rkA½H2Oꢃ
þk1;rk6;f kA½H2O2ꢃþk1;rk3;f kD½cycloocteneꢃþk1;rk3;rk5;r½diolꢃÞ
ðA:1Þ

K.R. Bjorkman et al. / Journal of Catalysis 291 (2012) 17–25
25
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kC ¼ k1;r þ k4;f
kD ¼ k4;f þ k5;f
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