Direct conversion of polyamides to ω-hydroxyalkanoic acid derivatives by using supercritical MeOH

Article abstract of DOI:10.1039/c1gc15172j

We examined the decomposition of polyamides such as nylon-6 and nylon-12 by using supercritical MeOH as the reaction media. The treatment of waste nylon-6 with supercritical MeOH resulted in smooth depolymerization, forming caprolactam as the first product which was then converted to a mixture of methyl 6-hydroxycapronate and methyl 5-hexenoate in a ratio of approximately 1:1. The reaction progress was traced using gas chromatography (GC) analyses, and precise product distribution was estimated. During the decomposition of nylon-6, N-methylcaprolactam and methyl 6-(N,N-dimethylamino)capronate were detected as intermediates. The sum of the all detectable products and intermediates exceeded 80%. In addition, we examined the decomposition reaction initiating from caprolactam, N-methylcaprolactam, and methyl N,N-dimethylcapronate under similar reaction conditions, and observed that the final two products were formed in similar yields and ratios. Kinetic analyses by using a simulation study based on the experimental data were performed, and kinetic parameters for each step were estimated. Nylon-12 underwent similar conversion to produce methyl 12-hydroxydodecanoate in good yield. Because methyl ω-hydroxyalkanoate is known to be an important intermediate in the chemical industry, the present method has the potential for producing valuable compounds from waste material. Thus, the first upgrade in the chemical recycling of plastics was accomplished.

Full text of DOI:10.1039/c1gc15172j

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PAPER
Direct conversion of polyamides to x-hydroxyalkanoic acid derivatives by
using supercritical MeOH
Akio Kamimura,*a Kouji Kaiso,a,b Shuzo Suzuki,a Yusuke Oishi,a Yuki Ohara,a,b Tsunemi Sugimoto,b
Kohichi Kashiwagib and Makoto Yoshimotoa
Received 15th February 2011, Accepted 20th April 2011
DOI: 10.1039/c1gc15172j
We examined the decomposition of polyamides such as nylon-6 and nylon-12 by using
supercritical MeOH as the reaction media. The treatment of waste nylon-6 with supercritical
MeOH resulted in smooth depolymerization, forming caprolactam as the first product which was
then converted to a mixture of methyl 6-hydroxycapronate and methyl 5-hexenoate in a ratio of
approximately 1 : 1. The reaction progress was traced using gas chromatography (GC) analyses,
and precise product distribution was estimated. During the decomposition of nylon-6,
N-methylcaprolactam and methyl 6-(N,N-dimethylamino)capronate were detected as
intermediates. The sum of the all detectable products and intermediates exceeded 80%. In addition,
we examined the decomposition reaction initiating from caprolactam, N-methylcaprolactam, and
methyl N,N-dimethylcapronate under similar reaction conditions, and observed that the final two
products were formed in similar yields and ratios. Kinetic analyses by using a simulation study
based on the experimental data were performed, and kinetic parameters for each step were
estimated. Nylon-12 underwent similar conversion to produce methyl 12-hydroxydodecanoate in
good yield. Because methyl w-hydroxyalkanoate is known to be an important intermediate in the
chemical industry, the present method has the potential for producing valuable compounds from
waste material. Thus, the first upgrade in the chemical recycling of plastics was accomplished.
their corresponding monomers, there are no known methods
Introduction
that directly convert polymers to compounds other than their
Polyamides such as nylon are used in our daily lives. Huge
monomers. In addition to these, current methods of monomer
amounts of them are continually manufactured and discarded
recycling are not always economically viable because this process
every year. In order to conserve carbon resources, waste
is usually more expensive than other methods for treating waste
polyamides should not be simply discarded but recycled through
plastics. If the process of the chemical treatment of waste plastics
an appropriate chemical process. Among the many recycling
could produce compounds or polymers more valuable than
methods so far developed, monomer recycling, which enables
simple reborn plastics, such process would offer increased value
rebuilt plastics to be prepared from waste plastics, is an ideal
and may solve the economic problems. However, to the best of
method for reaching this goal.1 The monomer recycling requires
our knowledge, there have been no such examples reported thus
the depolymerization process in which polyamides are converted
far.
to the corresponding monomer. The conversion of polyamides
During the course of our investigation on the development
to monomeric compounds has been previously investigated.2,3
of a new chemical recycling system for polyamide plastics,7 we
Hydrolysis by using supercritical or subcritical water was exam-
observed that the treatment of nylon-6 with supercritical MeOH
ined for this purpose, although monomeric amines and amino
resulted in the formation of methyl 6-hydroxycapronate and
acids were also decomposed under these reaction conditions.4
methyl 5-hexenoate in a selective manner, and not the anticipated
Thermolysis of polyamides5 and acid hydrolysis6 also offer
monomeric caprolactam. 6-Hydroxycapronic acid derivatives
good methods for the conversion. However, although these
are regarded as valuable chemical materials because the current
methods are useful for the conversion of the polymers to
average price of caprolactam, for example, is about 2.2 USD/kg,
while the average price of hydroxycarboxylic acid derivatives
(including 6-hydroxycapronic acid) is about 14.6 USD/kg (2008
aDepartment Applied Molecular Bioscience, Graduate School of
figures).8 This large price difference suggested that this process
Medicine, Yamaguchi University, Ube, 755-8611, Japan
bUbe Laboratory, Ube Industries Ltd., Ube, 755-8633, Japan
has the potential to become a new method for the formation
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of valuable compounds from valueless waste materials. To our
best of knowledge, this is the first economical upgrading of
polymers through the depolymerization process. We believe that
the present method will open new avenues in the development
of the chemical recycling of plastics. In this paper we report the
full details of the depolymerization of nylon-6 in supercritical
MeOH.
Results and discussion
Depolymerization of nylon-6 in supercritical MeOH
Nylon-6 and MeOH were added to a sealed stainless steel tube
and heated to 330 ◦C (Scheme 1). The pressure inside the
vessel increased to 27.0 MPa, around which MeOH achieved
its supercritical phase. We consider supercritical coordinates of
pure MeOH because the solute is present in small quantity
(7.5%w/w). The reaction vessel was maintained at the same
temperature for 6 h and then rapidly cooled using a dry-
ice/MeOH bath. The reaction mixture was then analyzed
using gas chromatography (GC). The reaction products were
identified by comparing the retention times and fragment
patterns in mass spectra with authentic compounds that are
usually commercially available. The GC analyses indicated that
the following six compounds were formed as main products in
the reaction: caprolactam 1, N-methylcaprolactam 2, methyl 6-
(N,N-dimethylamino)capronate 3, methyl 6-hydroxycapronate
4, methyl 5-hexenoate 5 and methyl 6-methoxycapronate 6
(Scheme 1). Although other small peaks in the GC were
observed, they could not be identified or quantified because
of their size. The main product yields were quantified by curve-
fitting methods, using 1-hexanol as an internal standard that was
added after the reaction. The yields were determined in chemical
yields per caprolactam unit, where, Yield (mol%) = products
(mmol)/amounts of caprolactam units (mmol) in nylon 6 ¥ 100
Amounts of caprolactam units (mmol) in nylon-6 = nylon-6
(mg)/113 (molecular weight of caprolactam 1)
Fig. 1 shows a typical course of the reaction of nylon-6 at
330 ◦C. The reaction mixture remained heterogeneous for the
first hour of the reaction, suggesting that the depolymerization
of nylon-6 was not yet completed and that insoluble oligomeric
polyamides still remained in the reaction mixture. A colourless
homogeneous solution was obtained after 1.5 h, indicating
that most of the polyamide was converted to monomeric
compounds. Caprolactam 1 was the main product in the early
stage of the reaction, with a yield reaching 30% after 1 h.
Thereafter, compounds 2 and 3 were formed as intermediate
products, and their yields increased gradually to reach peak
values approximately 2 h after the reaction started. The yield
Fig. 1 Treatment of nylon-6 in supercritical MeOH at 330 ◦C.
of compound 1 then decreased to approximately 0% after 3 h.
In the very early stage of the reaction, the final products,
compounds 4 and 5, were undetectable, but after 40 min their
yields increased in proportion to the reaction time, reaching
42% and 28%, respectively, after 4 h. The yields of compounds
4 and 5 thereafter remained at this maximum level, clearly
indicating that they remained stable and unchanged under
the reaction conditions. The product ratio of compound 4 to
compound 5 was approximately 1.5 : 1. We also attempted the
isolation of compound 4. The removal of MeOH under reduced
pressure resulted in oily products from which compound 5 was
readily removed because of its volatility. The chromatographic
purification of the residue resulted in pure compound 4 in 44%
yield. Compound 6 was detected after 3 h, although the yield
was still 3% after 6 h. The sum of the yields of all main products
and intermediates reached more than 80%, indicating that the
present product analyses have traced all of the main compounds
of the reaction.
We next examined this process for the decomposition reaction
of waste nylon-6 (Scheme 2). The waste nylon-6 was obtained
in a factory of nylon-6 as a residue of the distillation process.
It contained 78 wt% of oligomer of polyamide and 22 wt% of
caprolactam. Treatment of the waste (abt 0.3 g) with MeOH
(4 g) at 350 ◦C for 3 h resulted in the formation of a mixture
of decomposed products 1 to 6. The mixture was analyzed by
GC which showed that the yields of the products were 0.5%
for 1, 2% for 2, 0.8% for 3, 34% for 4, 33% for 5 and 0% for
Scheme 1 Depolymerization of nylon-6 with supercritical methanol.
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Table 1 Maximum yields of the products 1–6 during depolymerization of nylon-6 with supercritical MeOH
T/◦C
1; Yield (%)a
2; Yield (%)a
3; Yield (%)a
4; Yield (%)a
5; Yield (%)a
6; Yield (%)a
total yield (%)a
300
330
350
370
29(240)
27(80)
24(60)
20(40)
15(240)
14(120)
14(80)
12(40)
16(240)
12(100)
12(80)
13(40)
20(360)
42(300)
39(160)
40(100)
—b (—)
28(300)
31(160)
33(100)
n.d.c(—)
3(300)
6(360)
7(300)
77(240)
81(300)
80(160)
81(100)
a The yield was determined by GC analyses. The reaction time when reaching the maximum yield is shown in parentheses. b Not determined. c Not
detected.
Scheme 2 Depolymerization of waste nylon-6 in supercritical methanol.
Table 2 Yields of compounds 4, 5 and 6 through decomposition of
6. The reaction profile was very similar to the decomposition
reaction of pure nylon-6. Thus, the procedure was useful for
the depolymerization and chemical conversion process of waste
nylon-6.
nylon-6, and compounds 1, 2 and 3 in supercritical MeOH at 330 ◦C for
6 h
Starting
material 4; Yield (%)a 5; Yield (%)a 6; Yield (%)a Total yield (%)a
Mechanistic studies
Nylon-6 42
28
31
30
23
2
3
2
5
82
82
75
55
1
2
3
39
37
26
We next examined the conversion of nylon-6 at various temper-
atures. The peak yields of compounds 1 to 6 are summarized in
Table 1. The reaction conducted at other temperatures showed
a similar trend in product formation, as shown in Fig. 1. Thus,
compound 1 was formed as the first intermediate, and then the
yields of compounds 2 and 3 increased with decrease in the yield
of 1. Compounds 4 and 5 were then formed as final products.
The reaction at 300 ◦C progressed very slowly and an insoluble
polyamide oligomer was observed in the reaction mixture after
3 h. The reaction seemed to be incomplete even after 6 h because
the yields of compounds 4 and 5 remained at lower levels than
those achieved in subsequent reactions. When the reaction was
conducted at 350 ◦C, the reaction rate increased and the entire
reaction was completed within 3 h. The yields of compounds 4
and 5 reached 39% and 31%, respectively, after 160 min. These
values were similar to the yields achieved when the◦reaction was
a GC yields.
reaction to yield compound 4 and an elimination reaction
to yield compound 5. It should be noted that the yield
of compound 6 approached 0%, indicating that virtually
no substitution by MeOH occurred under these reaction
conditions.
The reactions initiating from compounds 1, 2 and 3 under
similar conditions at 330 ◦C were next conducted, and product
analyses were performed in a similar manner. The reaction
profiles are depicted in Fig. 2 to 4, and the results are summarized
in Table 2.
◦
performed at 330 C. However, the yields at 350 C gradually
decreased after 3 h, clearly indicating that the decomposition of
compounds 4 and 5 occurred under these reaction conditions.
The same trend was observed when the reaction was performed
at 370 ◦C. Although the reaction completed within 2 h, the
yields of compounds 4 and 5 decreased relatively rapidly than
those in the reaction at 350 ◦C. Thus, compounds 4 and
5 decomposed when exposed to temperature of 350 ◦C or
higher.
These results suggest a reaction pathway as shown in Scheme
3. Initially, the polymer linkage of nylon-6 was broken to
yield monomeric caprolactam 1. N-Methylation by supercritical
MeOH9 and ring opening subsequently occurred to yield
the intermediate compounds 2 and 3. The terminal amino
group in compounds 2 and 3 then performed a substitution
Scheme 3 Possible reaction pathway of depolymerization of nylon-6
with supercritical MeOH.
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Fig. 2 Treatment of caprolactam (compound 1) with supercritical
Fig. 4 Treatment of 6-N,N-dimethylcapronate (compound 3) with
MeOH at 330 ◦C.
supercritical MeOH at 330 ◦C.
compounds became the final products. The yields of compounds
4 and 5 reached 37% and 30%, respectively, which were almost
the equal to those in the reaction initiating from nylon-6.
The reaction initiating from compound 3 yielded compounds
4 and 5 directly, and no other intermediates were observed in
the reaction mixture (Fig. 4). The concentration of compound 3
rapidly decreased, and it was entirely consumed within 90 min.
The yields of compounds 4 and 5 finally reached 35% and 28%,
respectively.
Kinetic simulation
To analyze the kinetic behaviour of the reaction, we examined
a simulation of product distribution. For the analysis, we
postulated that the reaction progressed through the pathway
shown in Scheme 4, in which nylon-6 firstly gave caprolactam 1.
Caprolactam 1 underwent N-methylation and ring opening to
give compound 3 via compound 2. To simplify the simulation,
we treated the sum of the yields of compounds 2 and 3 as
the intermediate. Intermediate 3 was then converted to 6-
hydroxycapronate 4 via nucleophilic substitution or 5-hexenoate
5 via elimination reaction. Compound 6 was converted from
compound 4 but this reaction rate should be low because very
small amounts of 6 were formed in the actual reaction. The
degradation of nylon-6 into caprolactam 1 was regarded as
a first-order because the concentration of MeOH does not
change appreciably under the present reaction condition. Other
conversion steps were also considered to occur as a first-
order irreversible reaction. The calculations of the reaction
time courses were performed considering that the reaction
occurred in an isothermal batch reactor free of mass transfer
effect. The composition in the reactor changed with reaction
time (unsteady-state operation). The results are illustrated in
Fig. 5.
Fig. 3 Treatment of N-methylcaprolactam (compound 2) with super-
critical MeOH at 330 ◦C.
The treatment of compound 1 with supercritical MeOH at
330 ◦C resulted in the formation of compounds 2 to 6 (Fig. 2).
Compound 1 was consumed entirely after 4 h. Compounds 2 and
3 were formed in the early stage of the reaction and their yields
reached approximately 20% after 2 h. The yields of compounds
2 and 3 then gradually decreased and compounds 4 and 5 were
formed instead. The entire reaction was completed after 5 or
6 h, when the yields of compounds 4 and 5 were estimated to
be 39% and 31%, respectively. These yields were almost same
as the yields observed in the reaction from nylon-6. The sum
of the yields of all products exceeded 80%, indicating that most
reaction products were traced. Again, it should be noted that no
appreciable formation of compound 6 was observed.
The treatment of compound 2 under the same reaction
conditions yielded results similar to the reaction from compound
1 (Fig. 3). Thus, compound 2 disappeared after 4 h. Compound
3 was formed first and reached its peak yield in 100 min. The
yields of compounds 4 and 5 gradually increased, and those
The optimizations were performed by a downhill simplex
method using the software ‘ModelMaker’ obtained from Cher-
well Scientific Publishing Ltd, Oxford (the U.K.). Initially, we
attempted to use actual values for the simulation. However, we
encountered difficulties when fitting actual data, particularly at
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Scheme 4 Postulated reaction pathway for the depolymerization of nylon-6 in supercritical MeOH.
Fig. 5 Simulated profile of the reaction of nylon-6 in supercritical
MeOH at 330 ◦C. Circles and squares are based on the experimental
values and the lines are based on simulation.
Fig. 6 Temperature dependency of reaction rates (Arrhenius plots).
linear relationship between 1/T and lnkobs. Based on the slopes
calculated from Fig. 6, the activation energies for each step
were estimated to be 94.2 kJ mol-1 for the first step, nylon-6
to compound 1, 100.1 kJ mol-1 for the second step, N-alkylation
from compound 1, 84.8 kJ mol-1 for the formation of compound
4, and 94.4 kJ mol-1 for the formation of compound 5. Although
the N-alkylation step was slightly slower than the other steps, the
reaction rates and activation energies for all steps were in similar
value. Thus, the reaction progressed in a stepwise manner, such
that intermediates 1, 2, and 3 were observed in the reaction
mixture. The chemoselectivity between compounds 4 and 5 was
determined by the difference in the reaction rates between k3
and k4.
the very early stage of the reaction. An induction period at the
beginning of the reaction seemed to exist, possibly due to the
delay time during heating the reaction vessels to the desired
temperature. Indeed, we observed that 20–30 min was necessary
to increase the temperature of the reaction vessels above 300 ◦C.
We examined this delay in the simulations and finally determined
that introducing an induction period of 22 min provided a good
fit for the simulation. We performed this simulation for the first
118 min of the reaction. The coefficient showing the goodness-
of-fit was 0.983. Thus, the time course of each product fitted
well with the actual product distribution. The kinetic values for
the each reaction were estimated to be k1 = 1.47 ¥ 10-2 min-1,
k2 = 2.91 ¥ 10-2 min-1, k3 = 1.19 ¥ 10-2 min-1, and k4 = 8.16 ¥
10-3 min-1, respectively. The substitution/elimination ratio (4/5)
that was predicted from the kinetic values (k3/k4) was calculated
to be 1.46, which is close to the actual value of 1.5. The product
distribution of the reaction at different temperatures was also
simulated. The observed kinetic values, fitting coefficient and
induction periods are summarized in Table 3.
Depolymerization of nylon-12 in supercritical MeOH
Similar selective formation of methyl w-hydroxyalkanoate was
observed in the reaction of nylon-12 (Scheme 5). The treatment
of nylon-12 with supercritical MeOH at 330 ◦C resulted in a
smooth depolymerization of the polymer, as depicted in Scheme
5 and Fig. 7.
Considering these values, we next attempted to estimate the
activation energy parameter. The Arrhenius plots for these
values are illustrated in Fig. 6. The plots exhibit a good
The reaction progressed in a manner similar to that for
nylon-6. Methyl 12-(N,N-dimethylamino)laurate 7 was formed
as the intermediate, and then the conversion to methyl
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Table 3 Estimated kinetic parameters of the reaction
T/◦C
k1 (10-2 min-1)
k2 (10-2 min-1)
k3 (10-2 min-1)
k4 (10-2 min-1)
Induction time (min)
Coefficient
300
330
350
370
0.403
1.47
2.04
3.63
0.990
2.91
4.90
0.469
1.19
1.91
3.31
0.281
0.816
1.40
39
22
17
16
0.935
0.983
0.966
0.984
10.16
2.45
not decompose under the reaction conditions at 330 ◦C. A
kinetic simulation achieved an acceptable curve fitting when an
induction period was introduced, and the kinetic parameters for
each reaction were estimated. This procedure was useful for the
conversion of nylon-12 to corresponding hydroxyalkanoic acid
derivatives. Because the market value of hydroxyalkanoic acid
derivatives is higher than that of simple monomeric lactams, the
present procedure provides the first upgrading depolymerization
procedure for the chemical recycling of nylon-6. New devel-
opments in the recycling of plastics by using this concept are
anticipated. Further studies on this depolymerization procedure
are in progress in our laboratory.
Scheme 5 Depolymerization of nylon-12 with supercritical MeOH.
Experimental
Materials
Nylon-6 (Mw = 22 000) and nylon-12 (Mw = 30 000) were
supplied from Ube Industries as a gift. MeOH, reagent grade,
was purchased from Katayama chemical Inc. Osaka Japan,
All other chemicals were purchased from Aldrich or Tokyo
Chemical Industry (TCI).
Fig. 7 Treatment of nylon-12 with supercritical MeOH at 330 ◦C.
General procedures for depolymerization of nylon-6 in MeOH
12-hydroxylaurate 8 and methyl 11-dodecenoate 9 occurred.
Cyclic intermediates such as laurolactam were not observed,
possibly because the formation of the cyclic amide that requires
a large cyclic-ring formation from the open-chain monomer is
not easy. The total yield again exceeded 80%, such that almost
all reaction products were traced through the GC analysis. The
yield of compound 8 reached 59% after 5 h. It should be noted
that the methoxy derivative 10 was formed in approximately 4%.
The reaction temperature was also important. To obtain
12-hydroxycapronate 8 in good yield, 330 ◦C was the best
New nylon chips (0.3 g, Mw = 22 000) and MeOH (4 g)
were added to a 10 mL reaction vessel (7.35 mm id ¥ 23 cm
stainless tube, capped both ends by swagelok nuts) under argon
atmosphere. After sealing, the reaction vessel was placed in
a hot oven (300 to 370 ◦C) for the appropriate time. The
pressure reached 27.0 MPa. The reaction vessel was cooled with
dry-ice/MeOH bath, and 1-hexanol was added as an internal
standard. The products were analyzed by GC (Shimadzu GC-
2014, Intercap 5 (0.25 mm id ¥ 30 m) column) and quantified by
curve fitting methods.
◦
temperature. When the reaction was performed at 370 C, the
yield of 8 decreased as the reaction time was prolonged. On the
other hand, the reaction performed at 310 C took place very
◦
General procedures for depolymerization of nylon-12 in MeOH
slow and compound 8 was formed in 38% even after 6 h.
New nylon chips (0.3 g, Mw = 30 000) and MeOH (4 g) were
added to a 10 mL reaction vessel under argon atmosphere.
After sealing, the reaction vessel was placed in a hot oven
(330 ◦C) for the appropriate time. The reaction vessel was cooled
with dry-ice/MeOH bath, and dimethyl phthalate was added
as an internal standard. The products were analyzed by GC
(Shimadzu GC-2014, Intercap 5 (0.25 mm id ¥ 30 m) column)
and quantified by curve fitting methods.
Conclusion
We successfully developed a process for the direct conversion
of hydroxycapronic acid derivatives from nylon-6. The treat-
ment of nylon-6 with supercritical MeOH produced methyl
6-hydroxycaplonate 4 and methyl 5-hexenoate 5 in a 1.5 : 1
ratio. In this process, nylon was converted to methyl 6-
hydroxycaplonate 4, which is more valuable than caprolactam
1, the nylon-6 monomer. The reaction propagates through the
formation of caprolactam (compound 1), N-methylcaprolactam
(compound 2), and methyl N,N-dimethylcapronate (compound
3) as intermediates. Compounds 4 and 5 were stable and did
Isolation of methyl 6-hydroxycapronate (compound 4)
New nylon chips (0.3018 g, Mw = 22 000) and MeOH (4 g) were
added to a 10 mL reaction vessel under argon atmosphere. After
sealing, the reaction vessel was placed in a hot oven (330 ◦C) for
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6 h. The reaction vessel was cooled with dry-ice/MeOH bath.
MeOH was removed under reduced pressure and the residue was
purified through flash chromatography (silica gel/hexane–ethyl
acetate 10 : 1, then 1 : 1). Methyl 6-hydroxycapronate (compound
4) was isolated in 44% yield (0.1771 g, 1.212 mmol). Colourless
oil. 1H NMR dH (270 MHz, d3-CDCl3): 1.33–1.40 (2H, m,
–CH2–), 1.52–1.71 (4H, m, –CH2CH2–), 2.33 (2H, t, J = 7.6 Hz,
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–CH2-CO Me), 3.18 (1 H, s, OH), 3.58 (2H, t, J = 6.3 Hz, –CH2–
2
OH), 3.67 (3H, s, –CO2CH3); 13C dC (67.5 MHz, d3-CDCl3):
24.4 (C5), 25.1 (C4), 32.0 (C3), 33.7 (C2), 51.2 (–CO2CH3), 62.0
(C6), 174.1 (C1). HRMS (CI) [M + 1]: calculated for C7H15O3,
147.1021; observed 147.1021. Methyl 5-hexenoate (compound
5). 1H NMR dH (400 MHz, d3-CDCl3): 1.73 (2H, m, J = 7.3 Hz,
–CH2CH2CH2–), 2.09 (2H, q, J = 7.0 Hz, = CHCH2CH2CH2–),
2.32 (2H, t, J = 7.3 Hz, –CH2CO2Me), 3.67 (3H, s, CO2CH3),
4.96-5.05 (2H, m, CH2 CH–), 5.72–5.82 (1H, m, CH2 CH-);
13C dC (100 MHz, d3-CDCl3): 24.2 (C3), 33.2 (C4), 33.4 (C2),
51.6 (–CO2CH3), 115.5 (C6), 137.8 (C5), 174.1 (C1). MS (EI)
m/z 128 (M+, 30), 110 (19), 97 (35), 74 (100).
Parameter estimation and simulation
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Numerical integrations and optimizations by using the Runge–
Kutta method and Simplex algorithm, respectively, were per-
formed to estimate the kinetic parameters and to simulate the
reactions. The optimizations were performed by a downhill sim-
plex method using the software ‘ModelMaker’ obtained from
Cherwell Scientific Publishing Ltd, Oxford (U.K.). The objective
function is a residual sum of squares for minimization of the
difference between the calculated values and the experimental
data.
Acknowledgements
We are grateful to a financial aid from Yamaguchi University
based on The YU Strategic Program for Fostering Research
Activities (2010–2011).
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