Runge-Kutta analysis for optimizing the Zn-catalyzed transesterification conditions of MA and MMA with diols to maximize monoesterified products

Article abstract of DOI:10.1039/d1cy01180d

Terminal hydroxylated acrylates and methacrylates were prepared by catalytic transesterification of acrylates and methacrylates with diols catalyzed by a system of a tetranuclear zinc alkoxide, [Zn(tmhd)(OMe)(MeOH)]4 (1a), with 4 equiv. of 2,2′-bipyridine (L1). The reaction time to reach the equilibrium state was analyzed by kinetic studies and a curve-fitting analysis based on the Runge-Kutta method for optimizing the best reaction conditions for mono-esterification. In addition to these kinetic analyses, DFT calculations estimated a proposed mechanism of the catalytic transesterification. This journal is

Full text of DOI:10.1039/d1cy01180d

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Runge–Kutta analysis for optimizing the Zn-
catalyzed transesterification conditions of MA and
Cite this: DOI: 10.1039/d1cy01180d
MMA with diols to maximize monoesterified
products†
ab
Taito Kato,
Shin-ya Akebi,a Haruki Nagae, a Koji Yonehara,b
Tomoharu Okub and Kazushi Mashima
a
*
Terminal hydroxylated acrylates and methacrylates were prepared by catalytic transesterification of
acrylates and methacrylates with diols catalyzed by a system of a tetranuclear zinc alkoxide, [Zn(tmhd)
(OMe)(MeOH)]4 (1a), with 4 equiv. of 2,2′-bipyridine (L1). The reaction time to reach the equilibrium state
was analyzed by kinetic studies and a curve-fitting analysis based on the Runge–Kutta method for
optimizing the best reaction conditions for mono-esterification. In addition to these kinetic analyses, DFT
calculations estimated a proposed mechanism of the catalytic transesterification.
Received 2nd July 2021,
Accepted 19th August 2021
DOI: 10.1039/d1cy01180d
rsc.li/catalysis
zinc complex functioned as an appropriate catalyst for the
transesterification of methyl (meth)acrylate with a variety of
Introduction
Acrylates and methacrylates are highly attractive monomers,1
and their polymers are often used as polymeric resins,2
photoresists,3 and coating materials.4 These polymers exhibit
high transparency and flexibility as well as biocompatibility
and weatherability. The physical properties of poly(meth)
acrylates are introduced by replacing the ester moiety of the
monomers with any other preferred functional group.5 Among
functionalized (meth)acrylates, terminal hydroxylated (meth)
acrylates have attracted special attention because of their
hydrophilicity for emulsion paintings,6 UV reactive diluents,7
and adhesive compounds.8 Terminal hydroxylated olefinic
esters have been prepared by acylation of diol compounds with
(meth)acryloyl chlorides9 or transesterification of commercially
available methyl (meth)acrylate with diols,10 but difficulties
with the catalytic transesterification remain to be overcome,
including (1) a long reaction time to transesterification, (2) a
statistical mixture of terminal hydroxylated monomers and diol
bis(meth)acrylates, and (3) contamination by undesired side
reactions such as Michael addition11 and polymerization12 of
olefinic moiety. Thus, methods for selective mono-
esterification of (meth)acrylates with diols using efficient
catalytic systems under mild conditions are in high demand.
Herein, we report that a unique alkoxy-bridged tetranuclear
diols, such as 1,4-butanediol, leading to an equilibrium state of
a statistical mixture of terminal hydroxylated monomers and
diol bis(meth)acrylates. We also report that the yield of the
terminal hydroxylated monomers was maximized on the basis
of in-depth kinetic analysis and DFT calculations of the
reaction mechanism in which a mononuclear zinc catalyst
worked as an active species.
Results and discussion
The transesterification of carboxylic esters with alcohols
remains an essential synthetic method in organic chemistry,
and has been investigated using metal salt catalysts such as
Al,13 Ti,14 Sn,15 Zr,16 La,17 Zn,18 and Fe19 species. We
previously reported that a trifluoroacetate-bridged μ4-oxo-
tetranuclear zinc cluster, ZnTAC24®, served as an efficient
catalyst for the transesterification of methyl esters with
alcohols.20 In the first trial, we evaluated the catalytic activity
of ZnTAC24® with other commercially available Zn
mononuclear complexes as well as an alkoxy-bridged
tetranuclear complex (1a). Table 1 shows the results of the
catalytic transesterification of MA or MMA with diol 2a
mediated by 0.2 mol% of Zn precursors and 0.2 mol% of 2,2′-
bipyridyl in toluene at 85 °C for 3 h. The chemoselectivity of
the transesterification reaction was defined as the selectivity
of transesterification vs. Michael addition, and calculated by
dividing the provided amounts of the monoesters 3a and
diesters 4a by the converted amounts of MA or MMA. In the
case of the transesterification of MA, ZnTAC24® and
Zn(OAc)2 displayed low catalytic activity to afford monoesters
a Department of Chemistry, Graduate School of Engineering Science, Osaka
University, Toyonaka, Osaka 560-8531, Japan.
E-mail: mashima@chem.es.osaka-u.ac.jp
b Research Center, Innovation and Business Development Division, Nippon
Shokubai Co., LTD., Suita, Osaka 564-0034, Japan
† Electronic supplementary information (ESI) available. See DOI: 10.1039/
d1cy01180d
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Table 1 Comparison of the catalytic activity on several zinc precursors
Conv.a [%]
Yielda [%]
Entry
[M]
MA
2a
Chemoselectivityb [%]
Mono 3a
Di 4a
1
2
3
4
5
6
ZnTAC24®
Zn(OAc)2
Zn(acac)2
Zn(tmhd)2
Zn(hfac)2·H2O
[Zn(tmhd)(OMe)(MeOH)]4 (1a)
65
27
75
75
46
78
30
12
36
37
13
43
72
70
75
72
40
84
37
16
46
44
16
52
10
3
10
10
2
13
a
b
Determined by GC analysis with triphenylmethane as an internal standard. The chemoselectivity of transesterification reaction was
calculated as dividing the provided amounts of the monoesters 3a and diesters 4a by the converted amounts of MA.
3aMA in 37% and 16%, and diesters 4aMA in 10% and 3%
yields, respectively (entry 1–2). Other Zn mononuclear
complexes, such as Zn(acac)2 and Zn(tmhd)2, which have two
chelating acetylacetonate derivatives, exhibited more catalytic
activity than ZnTAC24® (entries 3–4), whereas Zn(hfac)2·2H2O
(HFAC = hexafluoroacetylacetonate) didn't display the same
catalytic performance probably affected by existing water.
Among several Zn precursors, the alkoxy-bridged tetranuclear
complex (1a) exhibited the highest catalytic activity and
highest chemoselectivity (entry 6) and was thus selected as
the best catalyst precursor.
We then started to compare the catalytic performance of
alkoxy-bridged tetranuclear complexes, [M(tmhd)(OMe)
(MeOH)x]4 (1a: M = Zn, 1b: M = Cu, 1c: M = Ni, 1d: M = Co, 1e:
M = Fe, and 1f: M = Mn; x = 1 or 0; tmhd = 2,2,6,6-tetramethyl-
3,5-heptanedione), for the transesterification of methyl acrylate
(MA) and methyl methacrylate (MMA) with 1,4-butanediol (2a)
to give the corresponding 4-hydroxybutyl (meth)acrylate (3aMA
and 3aMMA) and butane-1,4-diyl di[(meth)acrylate] (4aMA and
4aMMA) as a byproduct under the initial conditions (5.0 mmol
of MA or MMA, 7.5 mmol of 2a, 0.05 mol% of complexes 1a–f,
and 0.2 mol% of 2,2′-bipyridyl in toluene at 85 °C for 3 h), and
the results are presented in Table 2. In the reaction of MA with
2a, a zinc tetranuclear complex, [Zn(tmhd)(OMe)(MeOH)]4 (1a),
exhibited the highest catalytic activity and monoester/diester
ratio, 3aMA/(3aMA + 4aMA), to produce 3aMA in 52% yield with a
high chemoselectivity (entry 1), while tetranuclear complexes of
copper, nickel, and cobalt (1b–d) afforded 3aMA in low yield
with low chemoselectivity as these catalysts preferentially
mediated the Michael addition reaction of 2a with MA (entries
2–4). Manganese and iron tetranuclear complexes (1e and 1f)
exhibited moderate catalytic activities with moderate
chemoselectivities, yielding 3aMA in 39% and 36% yield,
respectively (entries 5 and 6). For the transesterification of
MMA, complex 1a also exhibited the highest catalytic reactivity
and chemoselectivity to give 3aMMA in 51% yield (entry 7).
Unfortunately, the use of copper complex 1b produced notable
side reactions of MMA. Complex 1b led to the polymerization
of MMA, probably because copper(II) ions activate the double
bond of MMA.21 When complexes 1c, 1d, and 1e were used, the
yields of 3aMMA decreased to 46%, 38%, and 19%, respectively,
and the chemoselectivity of the transesterification reaction was
lower than that when using zinc complex 1a (entries 9–11). The
use of manganese complex 1f also caused the polymerization
of MMA (entry 12), probably due to the softer ion character of
Mn(II), which prefers to interact with a softer CC double
bond than the carbonyl group of MMA. We also compared the
catalytic activity of complex 1a with a tin catalyst, SnO(n-oct)2,
which was used in several patents.22 The tin catalyst showed
much lower catalytic activity toward the transesterification of
MA or MMA with 2a than complex 1a throughout the
transesterification process over 10 h to an equilibrium of raw
materials and transesterified products. Among the six alkoxy-
bridged tetranuclear complexes and tin complex we tested, zinc
complex 1a exhibited the highest catalytic activity and
chemoselectivity as zinc(II) is the hardest metal ion on the basis
of the HSAB theory, and zinc(II) ions interact preferentially with
the carbonyl group, which is a harder functional group than
the double bond of MA. Considering all entries, we selected
zinc complex 1a as the best catalyst precursor among the
tetranuclear complexes, [M(tmhd)(OMe)(MeOH)x]4.
Next, we surveyed the best pyridine-based bi- and
tridentate ligands for the catalytic transesterification
reaction of MA and MMA with 2a. Table 3 provides the
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Table 2 Screening of alkoxy-bridged tetranuclear complexes
Conv.a [%]
Yielda [%]
Entry
R
Time. [h]
Cat.
(Meth)acrylate
2a
Chemoselectivityb [%]
Mono 3a
Di 4a
1
2
3
4
5
6
7
8
H
H
H
H
H
H
Me
Me
Me
Me
Me
Me
H
3
3
3
3
3
3
3
3
3
3
3
3
10
10
[Zn(tmhd)(OMe)(MeOH)]4 (1a)
[Cu(tmhd)(OMe)]4 (1b)
78
92
51
57
67
78
65
Gel.
57
52
27
Gel.
61
64
43
46
33
29
32
30
35
Gel.
26
21
9
84
10
18
46
65
60
>99
Gel.
93
90
80
Gel.
90
>99
52
8
8
13
1
2
9
7
[Ni(tmhd)(OMe)(MeOH)]4 (1c)
[Co(tmhd)(OMe)(MeOH)]4 (1d)
[Fe(tmhd)(OMe)(MeOH)]4 (1e)
[Mn(tmhd)(OMe)(MeOH)]4 (1f)
[Zn(tmhd)(OMe)(MeOH)]4 (1a)
[Cu(tmhd)(OMe)]4 (1b)
[Ni(tmhd)(OMe)(MeOH)]4 (1c)
[Co(tmhd)(OMe)(MeOH)]4 (1d)
[Fe(tmhd)(OMe)(MeOH)]4 (1e)
[Mn(tmhd)(OMe)(MeOH)]4 (1f)
Di-n-octyltin oxide
17
36
39
51
Gel.
46
38
19
Gel.
46
53
7
16
Gel.
7
8
2
Gel.
9
13
9
10
11
12
13
14
Gel.
24
29
Me
Di-n-octyltin oxide
a
b
Determined by GC analysis with triphenylmethane as an internal standard. The chemoselectivity of transesterification reaction was
calculated as dividing the provided amounts of the monoesters 3a and diesters 4a by the converted amounts of MA or MMA.
results of the experiments when using the best precursor 1a
with an equimolar amount of a pyridine-based ligand per
zinc atom at 85 °C for 3 h. Several ligands such as L1–L4
instead of pyridine-based derivatives were initially tested
with 1a, however, they were proved inadequate for the
transesterification with the zinc alkoxy-bridged tetranuclear
complex compared to 2,2′-bipyridine L6 (entries 2–5 vs.
entry 7). The use of pyridine ligand L5 and twice the
amount of 2,2′-bipyridine ligand had no effect to improve
activity or chemoselectivity (entries 6 and 8 vs. entry 7). The
electronic effects were surveyed using 4,4′-disubstituted 2,2′-
bipyridyl ligands, L7–L9 as well as 4,4′-dibromo-2,2′-
bipyridyl (L10), and we found that electron-donating groups
but lower catalytic activity and chemoselectivity were
observed (entries 18–19).
To improve the yield of the monoesters 3a, we further
modified the reaction conditions with the best catalyst 1a and
the best ligand L1, and the results are provided in Table 4. When
ether solvents, such as cyclopentyl methyl ether (CPME),
tetrahydrofuran (THF), and diethyleneglycol dimethyl ether
(diglyme), were used, the yield of monoester 3aMA was decreased
(entries 2–4 vs. 1). In comparison with entry 1 and entries 5–6,
increasing the equivalent of 2a versus MA improved the yield of
3aMA and the monoester/diester ratio. We also varied the
amount of the catalyst: the more catalyst loaded, the more the
Michael addition reaction proceeded, which means
chemoselectivity was decreased (entries 7 and 8). When the
reaction was conducted without complex 1a, no production of
3aMA was observed (entry 9). Entries 10–11 show how the
reaction temperature affected the transesterification reaction.
There was little change in the yield of 3aMA when the reaction
temperature was increased from 65 °C to 75 °C and 85 °C. We
adopted the same approach for MMA, and solvent changes
resulted in a decreased yield of the monoester 3aMMA with CPME
and gelation of the substrate mixtures with THF or diglyme
(entries 13–15 vs. 12). Increasing the equivalent of 2a versus
MMA in each 0.5 eq. from 1 to 2 eq. improved both the
monoester/diester ratio and total yield (entries 16 and 17 vs. 12),
and increasing the amount of loading catalyst 1a in each 0.1
mol% from 0.2 to 0.4 mol% finally led to gelation (entries 18
and 19 vs. 12). Entry 20 shows the result of the blank condition
and
halogen
slightly
decreased
the
yield
and
chemoselectivity of the transesterification reaction (entries
9–12). When an electron-withdrawing CF3 group was
introduced at the 5,5′-position of the 2,2′-bipyridyl ligand,
almost same yield and chemoselectivity as for L6 were
observed (entry 13). Entries 14–15 show the results of 6,6′-
substituted 2,2′-bipyridine, in which steric hindrance at the
6,6′-position reduced the catalytic activity compared with
the standard condition, and 6,6′-hydroxy bipyridine
completely blocked the transesterification (entry 15). We
also evaluated the influence of rotation of the principal axis
of 2,2′-bipyridine, by testing two phenanthroline ligands to
avoid the rotation, but it reduced the total yields of the
transesterification reaction (entries 16–17). In addition, we
used 2,2′-biquinoline and 2,2′:6′,2″-terpyridine as ligands,
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Table 3 Screening of ligands
Conv.a [%]
Yielda [%]
Entry
Ligand
X [mol%]
MA
2a
Chemoselectivityb [%]
Mono 3a
Di 4a
1
2
3
4
5
6
7
8
—
L1
L2
L3
L4
L5
L6
L6
—
62
62
85
33
67
64
78
78
81
80
77
72
74
60
n.r.c
80
77
44
89
33
26
37
10
40
37
43
32
30
37
36
34
31
30
n.r.c
42
29
19
51
91
58
44
0
46
26
32
—
10
10
6
—
7
8
13
9
8
9
10
10
11
11
n.r.c
8
11
6
4
0.2
0.2
0.2
0.2
0.4
0.2
0.4
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
67
80
84
66
62
66
73
79
84
96
n.r.c
60
79
70
34
38
43
52
43
42
44
46
47
51
46
n.r.c
40
50
24
25
9
L7
L8
L9
10
11
12
13
14
15
16
17
18
19
L10
L11
L12
L13
L14
L15
L16
L17
a
b
Determined by GC analysis with triphenylmethane as an internal standard. The chemoselectivity of transesterification reaction was
calculated as dividing the provided amounts of the monoesters 3a and diesters 4a by the converted amounts of MA. c No reaction.
in which the transesterification reaction did not proceed without
the zinc precursor 1a. The total yield of 3aMMA and 4aMMA
steadily increased simply by increasing the reaction temperature,
and side reactions such as the Michael addition reaction were
never observed around the these studied reaction conditions.
With the optimized conditions in hand, we investigated
the substrate scope of several diols, some of which contain
secondary and tertiary hydroxyl groups as non-equivalent
reaction sites (Table 5). We chose MMA as the other
substrate because MMA did not afford Michael addition
products. Ethylene glycol (2b) which has hydroxy groups at
the 1,2-positions reacted with MMA, but the yields of 3bMMA
and 4bMMA were very low (entry 2). In this case, we observed
white precipitates after the reaction, indicating that the
catalyst was deactivated by chelation of the 1,2-dihydroxy
moiety onto the zinc metal to give a stable 5-membered
metallacycle complex. The conversion of transesterification
increased readily with extension of the linker, and the
highest conversion was observed when we used 2a, whereas
extending one more methylene linker using 1,5-pentanediol
(2d) decreased the conversion to 58% (entry 4). Diol 2e,
which has primary and secondary hydroxy groups, mainly
afforded monoester 3eMMA (entry 5), indicating that the
sterically less hindered primary hydroxy groups were
approximately four times more reactive than the secondary
hydroxy groups. 1-Methyl-1,3-butandiol produced only
3-hydroxy-3-methylbutyl acrylate (3fMMA) in 18% yield over 3
h and 59% yield over 24 h, while diesterified byproduct
4fMMA was not observed. This result suggested that steric
hindrance of the tertiary hydroxy group protected against
conversion of the hydroxy group into the diester even over a
24 h reaction period (entries 6 and 7).
Kinetics study of the transesterification of (methyl)acrylate
and 1,4-butanediol
To clarify the reaction mechanism of the transesterification
of MA and MMA with 1,4-butanediol catalyzed by 1a with L1,
we conducted kinetic studies23 and tried to construct a
reliable kinetic model of this reaction. Scheme 1a–c shows
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Table 4 Screening reaction conditions
Conv.a [%]
Yielda [%]
Entry
R
Solvent
Y [equiv.]
Z [mol%]
Temp [°C]
(Meth)acrylate
2a
Chemoselectivityb [%]
Mono 3a
Di 4a
1
2
3
4
5
6
7
8
H
H
H
H
H
H
H
H
Toluene
CPME
THF
1.5
1.5
1.5
1.5
1
2
2
2
2
0.2
0.2
0.2
0.2
0.2
0.2
0.3
0.4
—
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.3
0.4
—
85
85
85
85
85
85
85
85
85
65
75
85
85
85
85
85
85
85
85
85
65
75
78
83
78
62
72
81
82
84
10
64
80
65
43
34
34
26
44
33
36
36
6
24
32
35
84
56
76
58
87
85
77
73
24
93
77
>99
96
Gel.
Gel.
>99
92
52
40
48
26
46
57
53
52
2
51
52
51
44
—
—
37
53
54
—
—
20
40
13
7
11
10
17
11
10
10
0
Diglyme
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
CPME
9
H
H
H
10
11
12
13
14
15
16
17
18
19
20
21
22
2
2
9
9
Me
Me
Me
Me
Me
Me
Me
Me
Me
Me
Me
1.5
1.5
1.5
1.5
1
16
12
—
—
16
12
17
—
—
3
58
28
THF
Gel.
Gel.
52
71
76
Gel.
n.r.c
23
Gel.
Gel.
41
30
35
Gel.
n.r.c
13
Diglyme
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
2
1.5
1.5
1.5
1.5
1.5
94
Gel.
n.r.c
99
0.2
0.2
47
21
>99
9
a
b
Determined by GC analysis with triphenylmethane as an internal standard. The chemoselectivity of transesterification reaction was
c
calculated as dividing the provided amounts of the monoesters 3a and diesters 4a by the converted amounts of MA or MMA. No reaction.
Table 5 Substrate scope of diols
Yielda,b [%]
Entry
Diol 2
Time [h]
Conv. [%]
Monoester 3
Diester 4
1
2
2a
2b
3
3
65
24
3aMMA
51
15
4aMMA
16
1
(3b)
(4b)
(4c)
(4d)
(4e)
3
4
5
2c
2d
2e
3
3
3
31
58
26
(3c)
25
42
16
4
(3d)
11
1
(3e)
3
(3e′)
(3f)
6
7
2f
2f
3
24
18
59
18
59
a
Determined by GC analysis with triphenylmethane as an internal standard. b Calculated via FID relative sensitivity of each compound.
the proposed elementary reactions of this esterification
process. The methyl (meth)acrylate (ME) and 2a are converted
into the monoester (Mono) and MeOH under the rate
constant k1, and in the reverse reaction, the rate constant
and equilibrium constant are expressed as k−1 and K1
(Scheme 1a). In the same manner, the second
transesterification proceeds with Mono and ME into the
diester (Di) and MeOH, and the rate constant of each forward
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between K1, K2, and K3 is described in below (eqn (6)).
2
K1 ½Monoꢀ½MeOHꢀ ½Diꢀ½MEOHꢀ ½Monoꢀ
¼
÷
¼
¼ K3 (6)
K2
½MEꢀ½BDꢀ
½Monoꢀ½MEꢀ ½BDꢀ½Diꢀ
In the case of MA, the initial reaction was conducted
under the following standard conditions26 (a): [MA]0/[2a]0/[1a]
(calculated on metal ions) = 3.10 [mol kg−1]/6.19 [mol kg−1]/
8.26 [mmol kg−1], where [X]0 is the initial concentration of X.
Under condition (a), the following rate constants were
determined: k1 = 23.0, k−1 = 15.1, k2 = 18.9, k−2 = 63.3, k3
=
103, k−3 = 20.1 [kg2 mol−2 h−1]. To ensure the accuracy of the
rate constants calculated under standard conditions,
equivalents of 2a and 1a against MA were changed to the
following conditions: [MA]0/[2a]0/[1a], (b) = 3.72 [mol kg−1]/
5.58 [mol kg−1]/8.26 [mmol kg−1], (c) 2.64 [mol kg−1]/6.61 [mol
kg−1]/8.26 [mmol kg−1], (d) 3.10 [mol kg−1]/6.19 [mol kg−1]/
12.4 [mmol kg−1], (e) 3.10 [mol kg−1]/6.19 [mol kg−1]/16.5
[mmol kg−1]. In addition, to estimate the activation energies,
the standard enthalpy change (ΔH), and the standard entropy
change (ΔS), two other conditions with different temperatures
were used with the same initial concentrations as in
condition (a), (f) 65 °C, (g) 75 °C. Fig. 1 shows the
experimental data (plots) and simulated results (lines), which
were well fitted to the experiments and in accordance with
the proposed kinetic model described in Scheme 1. All plots
of conditions (b)–(e) are expressed by the set of the reaction
rates k1, k−1, k2, k−2, k3, and k−3, which were estimated from
condition (a). Thus, it is possible to predict how much MA
and 2a transformed into Mono and Di at a certain catalyst
concentration and a certain temperature from the initial
concentrations of raw materials.
Scheme
1 Elementary reactions of transesterification process
between methyl (meth)acrylate and 1,4-butanediol.
and inverse reaction as well as the equilibrium constant are
denoted as k2, k−2, and K2 (Scheme 1b). Moreover, in the
presence of Di and 2a, these compounds are transformed
into 2 equiv. of Mono with rate constant k3, and we termed
the rate constant of the inverse reaction and the equilibrium
constant of each as k−3 and K3 (Scheme 1c). We confirmed
that complex 1a catalyzed all six elementary reactions of
methyl acrylate by comparing the initial reaction rate of six
elementary reactions with and without a catalytic amount of
complex 1a.15 Especially in the case of MA, we considered
four other elemental reactions with the rate constants k4, k5,
k6, and k7 to give four byproducts in very low yields, because
several byproducts derived via Michael addition reaction were
observed in GC and MS analyses (see ESI†). On the basis of
the above-described kinetic model, the five ordinary
differential equations for ME, 2a, Mono, Di, and MeOH (eqn
(1)–(5)) as well as four additional ordinary differential
equations for byproducts only in the case of MA were solved
numerically for all simulations in this study.
Next, we estimated the activation energies (Ea1, Ea−1, Ea2,
Ea−2, Ea3, and Ea−3) for the formation of Mono and Di from
datasets in the conditions of (a), (f), and (g). The activation
energy (Ea) was estimated using Mathcad software on the
The rate law is expressed by a reaction time (t[h]) and the
rate constants for each compound were as follows:24
d½MEꢀ
¼ ½catꢀð−k1½MEꢀ½2aꢀ þ k ½Monoꢀ½MeOHꢀ − k2½MEꢀ½Monoꢀ þ k ½Diꢀ½MeOHꢀ þ BPME
Þ
−1
−2
(1)
(2)
dt
(1)
À
Á
d½2aꢀ
2
¼ ½catꢀ −k1½MEꢀ½2aꢀ þ k ½Monoꢀ½MeOHꢀ − k3½2aꢀ½Diꢀ þ k ½Monoꢀ þ BPBD
−1
−3
dt
(2)
À
À
Á
Á
d½Monoꢀ
dt
2
¼ ½catꢀ k1½MEꢀ½2aꢀ − k ½Monoꢀ½MeOHꢀ − k2½MEꢀ½Monoꢀ þ k ½Diꢀ½MeOHꢀ þ 2 k3½2aꢀ½Diꢀ − k ½Monoꢀ þ BPMono
−1
−2
−3
(3)
(4)
(5)
(3)
À
Á
d½Diꢀ
dt
2
¼ ½catꢀ k2½MEꢀ½Monoꢀ − k ½Diꢀ½MeOHꢀ − k3½2aꢀ½Diꢀ þ k ½Monoꢀ þ BPDi
−2
−3
(4)
d½MeOHꢀ
dt
¼ ½catꢀðk1½MEꢀ½2aꢀ − k ½Monoꢀ½MeOHꢀ þ k2½MEꢀ½Monoꢀ − k ½Diꢀ½MeOHꢀ þ BPMeOH
Þ
−1
−2
(5)
For further investigation, Runge–Kutta curve-fitting
analysis using Mathcad software25 was conducted based on
the experimental data of GC analysis on ME, 2a, Mono, and
Di, and the other details are presented in ESI.† The basic five
plus additional four (only in the case of MA) ordinary
differential equations generated were solved numerically for
all the simulations in this study, where the relationship
basis of the Arrhenius equation, in which kT (rate constant at
T °C) is expressed as kT′ = kT exp[(Ea/R){1/T} − (1/T′)]. The
activation energies were determined to be Ea1 = 55.1, Ea−1
=
39.7, Ea2 = 49.7, Ea−2 = 33.0, Ea3 = 39.9, Ea−3 = 41.2 [kJ mol−1].
Finally, ΔH values and ΔS values were calculated from the
estimated values of K65, K75, and K85 by van't Hoff plot based
on the van't Hoff equation, ln(KT) = −ΔH/RT + ΔS/RT. As the
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Fig. 1 Curve-fitting calculations for the transesterification of MA and 1,4-butanediol and estimated kinetic parameters using [Zn(tmhd)(OMe)
(MeOH)]4 as the catalyst in toluene.
result, we determined the ΔH and ΔS of the
mol−1]; ΔS1′ = 50.6/ΔS2′ = 39.8/ΔS3′ = 10.8 [kJ mol−1]; ΔG1′ =
−2.77/ΔG2′ = −1.59/ΔG3′ = −4.36 [kJ mol−1] (Fig. 2).
transesterification using MA as follows: ΔH1 = 15.4/ΔH2
16.7/ΔH3 = −1.36 [kJ mol−1] and ΔS1 = 46.8/ΔS2 = 36.3/ΔS3
=
=
To clarify the mechanism of this esterification reaction,
DFT calculations27 were performed with the dispersion-
corrected B3LYP functional using MA and 2a as
representative substrates. Although in the previous
transesterification using [Zn4(OCOR)6O],20c we proposed
mechanisms mediated by multinuclear complexes; in the
case of an alkoxide-bridged cluster, a dinuclear pathway
produced much higher energy than a mononuclear pathway
(see ESI†). Thus, we excluded the dinuclear pathway and
proposed the catalytic cycle by the zinc mononuclear complex
(Fig. 3a). The alkoxide-bridged tetranuclear zinc cluster 1a is
dissociated to four mononuclear complexes by the
coordination of L1. Methoxide is then exchanged with 2a to
give MeOH and complex A as catalytically active species. The
first step of the transesterification is the coordination of MA
to the zinc atom of complex A to form B, which has 23.5 kJ
mol−1 higher energy than A. Then, intramolecular
nucleophilic attack of the terminal alkoxide occurs to a
carbonyl carbon of the coordinating MA via transition state
TS1, leading to intermediates D via C. The free energy of TS1
is 54.4 kJ mol−1 relative to the starting point at A, and the
free energies of intermediates C and D are 53.6 kJ mol−1 and
10.5 [kJ K−1 mol−1].15 ΔG was also determined based on the
calculated values of ΔH and ΔS at 85 °C as follows: ΔG1
=
−1.41/ΔG2 = 3.70/ΔG3 = −5.11 [kJ mol−1], which revealed a
small energy gap between the substrates and products
converting
reversibly
under
this
equilibrium
transesterification reaction.
In the same way, the rate constants and kinetic- and
thermodynamic parameters for the transesterification of
MMA were estimated under the 7 conditions shown below:
[MMA]0/[2a]0/[1a], (a′) = 3.91 [mol kg−1]/5.86 [mol kg−1]/7.82
[mmol kg−1], (b′) = 4.30 [mol kg−1]/4.30 [mol kg−1]/7.82 [mmol
kg−1], (c′) = 3.28 [mol kg−1]/6.57 [mol kg−1]/7.82 [mmol kg−1],
(d′) = 3.91 [mol kg−1]/5.86 [mol kg−1]/11.7 [mmol kg−1], (e′) =
3.91 [mol kg−1]/5.86 [mol kg−1]/7.82 [mmol kg−1], as well as
two conditions using the same initial concentrations as in
condition (a′) but at different temperatures, (f′) 65 °C, (g′) 75
°C. As a result, we determined the rate constants as, k1′ =
9.58/k−1′ = 5.61/k2′ = 15.4/k−2′ = 38.6/k3′ = 78.9/k−3′ = 18.4 [kg2
mol−2 h−1], and kinetic- and thermodynamic parameters as,
Ea1′ = 84.6/Ea−1′ = 69.2/Ea2′ = 63.2/Ea−2′ = 47.4/Ea3′ = 53.3/Ea−3
′
= 53.8 [kJ mol−1]; ΔH1′ = 15.4/ΔH2′ = 15.9/ΔH3′ = −0.50 [kJ
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Fig. 2 Curve-fitting calculations for the transesterification of MMA and 1,4-butanediol and estimated kinetic parameters using 1a as the catalyst in
toluene.
44.6 kJ mol−1, respectively. The C–O bond cleavage proceeds
via transition state TS2, resulting in the formation of E, and
the calculated barrier for this concerted C–O bond cleavage
step is 54.2 kJ mol−1 relative to complex A. The monoester
3aMA and MeOH are released in the next step together with
an intermolecular ligand exchange with additional 2a, and
finally complex A is regenerated.
To continuously produce monoester preferentially, it is
necessary to search for the best condition affording the
maximum amount of monoester per unit of time. Thus, we
demonstrated the reaction yield estimation based on kinetic
parameters obtained by Runge–Kutta curve-fitting analysis
(vide supra). The productivity, chemoselectivity, and yields of
3aMA and 3aMMA were plotted versus temperature
(Fig. 4a, b, d and e) and equivalents of 2a (Fig. 4c and f). As
shown in Fig. 4a, the kinetic model suggests that raising the
was defined when the yield of monoester 3aMA reached the
highest value under a certain condition. The simulated
kinetic model enabled us to determine the equilibration
time depending on the initial condition, so the reaction
condition was set as follows: [1a] (on metal ions) = 8.26
[mmol kg−1] (in the case of MA), the molar mass of toluene
was 100 times larger than [1a]. The details of the simulated
data are provided in the ESI.† In the case of MA, 1.2 equiv.
of 2a provided the maximum yield of monoester 3aMA (2.29
mol kg−1) (Fig. 4c). The kinetic model of MMA suggests that
increasing the reaction temperature is also a straightforward
approach to obtaining monoesterified product 3aMMA in
high yield (Fig. 4d) but this approach would decrease the
ratio of 3aMMA/4aMMA and reach a minimum value at 110 °C
(Fig. 4e). Thus, we fixed the reaction temperature to 85 °C
and 105 °C for MMA, and set the reaction conditions as
follows: [1a] (on metal ions) = 7.82 [mmol kg−1] (in case of
MMA), the molar mass of toluene was 100 times larger than
[1a], and then searched for the best equivalent of 2a versus
MMA according to the simulated kinetic model under a
certain condition. In the case of MMA, 1.3 equiv. of 2a
would afford the maximum yield of the monoester 3aMMA as
2.20 [mol kg−1] at 85 °C and 2.37 [mol kg−1] at 105 °C
(Fig. 4f).
reaction temperature is
a straightforward approach to
obtaining monoesterified product 3aMA in high yield in the
case of MA. A higher reaction temperature over 80 °C,
however, increases the risk of polymerization of MA and
decreases the ratio of 3aMA/4aMA. Accordingly, we fixed the
reaction temperature to 85 °C for MA. We then started to
search for the best equivalent of 2a versus MA according to
the simulated kinetic model, in which an equilibration time
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Fig. 4 Optimizing reaction conditions estimated by kinetic models. (a)
Temperature effect on 3aMA productivity [mol kg−1 h−1)]. (b)
Temperature effect on 3aMA/4aMA ratio. (c) 2a equivalent effect to
3aMA yield [mol kg−1]. (d) Temperature effect on 3aMMA productivity
[mol kg−1 h−1)]. (e) Temperature effect on 3aMMA/4aMMA ratio. (f) 2a
equivalent effect on 3aMMA yield [mol kg−1].
yield, respectively. The estimated value derived from the
kinetic model and the experimental result for MMA also
matched well. These results demonstrated that the reaction
yield estimation based on kinetic studies could be reliably
applied to predict the equilibrium state. This modeling
Fig. 3 a) Proposed reaction mechanism and b) calculated free energy
profile (kJ mol−1) for the transesterification of MA and 2a mediated by
the zinc mononuclear complex in toluene.
Using the simulated best conditions, at 85 °C with 1.2
equiv. of 2a for MA or at 85 °C and 105 °C with 1.3 equiv. of
2a for MMA, we confirmed the accuracy of these kinetic
models and reaction yield estimation by collecting
experimental data for MA and MMA. When MMA was used as
substrate, 50 ppm of 4-hydroxy-TEMPO free radical against
MMA was added to prevent the polymerization because MMA
required a longer reaction time to reach the equilibrium
state. Fig. 5 shows an excellent correlative relationship
between the estimated value derived from the kinetic model
and the experimental result at 85 °C: the actual yields of
3aMA and 4aMA were 48.0% and 15.1% yield, respectively, and
the estimated yields of 3aMA and 4aMA were 48.4 and 14.9%
Fig. 5 A demonstration experiment of optimal reaction conditions
based on kinetic models.
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would be useful for predicting the compositional ratio of a
crude mixture among MA, MMA, 2a, 3a, and 4a in each
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Conclusions
In summary, we developed a new, efficient transesterification
of methyl(meth)acrylates and diol compounds catalyzed by
unique cubic cluster complexes and a 2,2′-bipyridine ligand
system containing first-row late-transition metal centers.
[Zn(tmhd)(OMe)(MeOH)]4 was selected as the best precursor
in terms of not only its catalytic activity but also its
chemoselectivity for minimizing the influence of side
reactions, such as the Michael addition reaction. We also
describe our attempts to unravel the reaction mechanism of
this equilibrium transesterification reaction and suggest a
model that the Zn(II) mono-nuclear complex is generated to
become a real active species by the cubane precursor and the
bipyridine ligand. Moreover, kinetic studies and precise
calculations based on the Runge–Kutta method for curve-
fitting analysis were conducted, and the derived kinetic
parameters totally support the model presented above. Thus,
we demonstrated the usefulness and potential to combine
kinetic studies via curve-fitting analysis and computational
DFT calculations to enhance the reliability of the suggested
reaction mechanisms. Further studies to apply these findings
to industrial synthesis are ongoing in our laboratory.
Author contributions
T. K. wrote the manuscript with support from H. N. and K.
M., and T. K. carried out experiments, kinetic study, and
curve-fitting analysis. H. N. conducted the DFT calculations.
S. A. contributed to the initial studies in an early stage of the
project. K. Y., T. O. and K. M. supervised the project.
Conflicts of interest
There are no conflicts to declare.
Acknowledgements
We thank Mr. Motosuke Imada and Mr. Yasutaka Sumida of
the research center at Nippon Shokubai Co., Ltd. for assistance
and advice regarding the Runge–Kutta method curve-fitting
analysis and for arranging the framework of this project.
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