1
98
A. Kosaka et al. / Journal of Molecular Structure 1093 (2015) 195–200
Fig. 4. 1H NMR chart of (a)
a-mannose and (b) b-mannose in D O.
2
which is also consistent with the value of 1.84–2.01 kJ mol 1 deter-
ꢁ
Table 2
Chemical shift of the 1H signals for
a- and b-mannose.
mined by GLC and OR [14]. Quantum chemical calculations have
suggested that in the gas phase the a-anomer of both glucose and
Chemical shift/ppm
-mannose
Assignment Literature
18]
mannose is more stable than the b-anomer, in which the O–H
groups forms the intramolecular hydrogen-bond [20]. In water,
the OH groups of glucose and mannose may change their orienta-
tions because of the hydration, implying that the stability of b-glu-
cose is owing to the hydration. The hydration effects on the stability
a
b-mannose
This
study
Splitting Literature
[18]
This
study
Splitting
[
H1
H2
H3
H4
H5
H6a
H6b
5.05
3.79
3.72
3.52
3.70
3.74
3.63
5.05
3.80
3.71
3.52
3.68
3.74
3.62
d
4.77
3.85
3.53
3.44
3.25
3.74
3.60
4.77
3.82
3.53
3.45
3.26
3.78
3.60
d
dd
dd
dd
ddd
dd
dd
dd
dd
dd
ddd
dd
dd
of the anomers may be different for glucose and mannose.
1
The H NMR spectra of
a
- and b-glucose show the time-
dependent changes caused by anomerization. To monitor the
population of both monomers, we chose the H1 proton of -glucose
a
and H2 of b-glucose, because they are well isolated from the other
proton signals as shown in Fig. 3. Note that the H1 proton signal of
b-glucose is not used, because the peak is located at the lower
interaction between H2 and H4. That is, the orientational change in
the C2–H2 may affect the chemical shift of H4.
slope of the proton signal of the residual H
the time-dependent change in the mole fraction of the
ꢁg(t) during the anomerization starting from the -anomer. The
value of x ꢁg(t) monotonically decreases as a function of time.
2
O. Fig. 5(A) shows
a-glucose
In order to investigate the C5–C6 rotamers of a- and b-mannose,
x
a
a
the coupling constant between H5 and H6b for mannose has to be
determined. The peaks of H5 and H6b split into ddd and dd, respec-
tively. The coupling constant between H5 and H6b for both the
anomers is obtained from the 1H NMR spectra shown in Fig. 4.
The value of JH5H6b is 5.9 Hz, indicating that the O5–C5–C6–O6
dihedral angle is one of the following: ca. 8°, 95°, 165°, or 96°.
a
Fig. 5(B) represents the time-dependent change in the mole frac-
tion of the b-glucose xbꢁg(t) during the anomerization starting from
the b-anomer, and a monotonic decrement is also found. The
a
decrement of x ꢁg(t) and xbꢁg(t) becomes steep when the tempera-
ture increases as shown in Fig. 5, indicating that the reaction rate
gets high. The reaction rate constant, k, can be evaluated by the
least square fitting with using the following single exponential
equation,
Again, the calculation result [18] implies that / = 8° is unrealistic.
3
Note that the quantity of
JH5H6a is 1.9 Hz in consistency with the
3
3
J
H5H6b quantity. For b-mannose,
Although these values are not so far from those observed for
-mannose, it is suggested that the O5–C5–C6–O6 dihedral angle
of -mannose is slightly larger than that of b-mannose.
JH5H6b of 6.3 Hz is obtained.
xðtÞ ¼ ðx
where x
0
ꢁ xeqÞ expðꢁktÞ þ xeq
ð3Þ
a
a
0
is the initial mol fraction of anomer and xeq is the mole
fraction at equilibrium. In the anomerization process of mannose,
we used the integral intensity of the H1 proton of -mannose and
that of H5 of b-mannose to monitor the population change. The
time-dependent change in the mole fraction of the -mannose
ꢁm(t) is recorded at a different temperature as shown in Fig. 6.
Thermodynamic parameters of the anomerization for glucose and
mannose
a
a
The difference in the standard Gibbs energy of the anomeriza-
x
a
tion from
a- to b-anomer
D
r
G
a
?b can be calculated from the equi-
All the time profiles can also be fitted by Eq. (3) and the quantities
of k are determined.
librium constant K = [b]/[
a] by using the following equation.
In order to estimate thermodynamic properties, we employ the
Arrhenius and Eyring plots. Since the reaction rate is possibly
affected by surrounding aqueous media, we must consider that
the parameters determined here may contain the influence from
the hydration of compounds. At the same time, however, we can
also expect that the hydration state of compounds does not signifi-
cantly change because of the temperature range. First, the activa-
½
bꢂ=½ ꢂ ¼ expðꢁ !b=kTÞ
a
D
r
G
a
ð2Þ
where k is the Boltzmann constant, T is the absolute temperature,
[
a
] is the mol fraction of the -anomer at the equilibrium, and [b]
is that for the b-anomer. As a result,
obtained for glucose, suggesting that the b-glucose is more stable
in the aqueous solution. The ?b quantity obtained here is in
good agreement with that previously reported by the use of GLC
a
ꢁ
1
D
r
G
a
?b = ꢁ1.3 kJ mol
is
r a
D G
a
tion energy of anomerization (E ) for glucose and mannose is
estimated by the Arrhenius Plots. As shown in Fig. 7(A), a linear
1
and OR [14]. On the other hand,
D
r
G
a
?b of 1.8 kJ mol for mannose
indicates that the -anomer is more stable in aqueous solution,
a
relationship between ln(k) and 1/T fits quite well for both