Analysis of Intermolecular Interaction among Pectin ... · tin solutions (Pippen et al., 1953;...
Transcript of Analysis of Intermolecular Interaction among Pectin ... · tin solutions (Pippen et al., 1953;...
Analysis of Intermolecular Interaction among Pectin Molecules in Aqueous Sugar
Solutions
Yukinori Sato1* and Osato miyawaKi
2
1 Laboratory of Food Science and Technology, Kochi Women's University, Eikokuji 5-15, Kochi 780-8515, Japan2 Department of Food Science, Ishikawa Prefectural University, Suematsu 1-308, Nonoichi, Ishikawa 921-8836, Japan
Received April 26, 2007; Accepted January 28, 2008
Although the viscosity of aqueous solution of high methoxyl pectin is known to increase drastically when sugars coexist, the detailed mechanism for the increase in viscosity was not fully understood. There-fore, the viscosity of citrus and apple pectin solutions with various sugars compositions was measured with temperature varying from 5 to 40℃ to analyze the intermolecular interactions among pectin mol-ecules. For single-composition pectin solutions, the activation energy for viscosity, Ea, increased from 17.5 to 31.9 kJ/mol with an increase in pectin concentration up to 2% for the case of citrus pectin, reflecting the increase in pectin-pectin interaction. For pectin solutions with coexisting sugars, Ea increased more with increasing sugar concentration. When compared at the same water activity, the increase in Ea is also dependent on the type of sugar. Sugars with stronger solvent-ordering activity produced greater increases in Ea. These results suggest that sugars increase the pectin-pectin interaction both through their own hy-dration effect, which enhances the hydrogen bonding among pectin molecules, and through the solvent-ordering effect to enhance the hydrophobic interaction.
Keywords: pectin, viscosity, activation energy, hydrogen bonding, hydrophobic interaction
*To whom correspondence should be addressed.
Email: [email protected]
IntroductionPectin is a hydrocolloid predominantly comprising ga-
lacturonic acid and its methyl ester form, and it has been
frequently utilized in food applications including as a gelling
agent and thickener (Thakur et al., 1997). Physical properties
of pectin solutions depend on the molecular size of pectin
molecules (Ishihara, 1992), the degree of methoxylation (Pip-
pen et al., 1953; Oakenfull and Scott, 1984), the degree of
dissociation of carboxylic groups (Michel et al., 1982), sub-
stituents of the carboxyl groups (Axelos and Thibault, 1991),
and the rhamnose content in the pectin molecule (Axelos and
Thibault, 1991). In addition, the solvent properties character-
ized by pH, ionic strength, and the solvent-ordering also play
important roles in determining the physical properties of pec-
tin solutions (Pippen et al., 1953; Oakenfull and Scott, 1984;
Chen and Joslyn, 1967; Sato et al., 2004).
When methoxyl content is low, the solution property of
pectin is dependent on the ionic linkages via carboxyl groups
belonging to different chains to form a structure resembling
an egg-box (Thakur et al., 1997). When methoxyl content
is high, the solution properties of pectin are known to be
strongly affected by the coexistence of sugars (Chen and
Joslyn, 1967; Crandall and Wicker, 1986; Kar and Arslan,
1999a; Bulone et al., 2002; Fishman et al., 2004; Sato et al.,
2004). However, the detailed mechanism of the effect of sug-
ars has been not fully understood.
In this paper, the viscosity of pectin solutions with vari-
ous sugars is systematically measured by changing sugar
concentration and temperature. The activation energy for
viscosity was obtained at various conditions to analyze the
intermolecular interactions among pectin molecules.
Materials and MethodsMaterials Glucose and sucrose were obtained from Na-
calai Tesque, Co. (Kyoto, Japan), mannose and maltose from
Wako Chemical Industries (Osaka, Japan), trehalose from
Tokyo Kasei Organic Chemicals (Tokyo, Japan), and ribose
from Sigma (St. Louis, MO, USA). For all the sugars, the
water content was analyzed by drying in oven at 110-120℃
Food Sci. Technol. Res., 14 (3), 232–238, 2008
233
to accurately calculate the sugar concentration.
Pectins from citrus and apple fruits were purchased from
Sigma. According to the technical data attached, the galact-
uronic acid and metoxyl content for the citrus pectin were
79.5% and 8.1% (DM, degree of esterification = 57.9%),
respectively. For the apple pectin, these were measured to
be 79.0% and 8.7% (DM=62.1%), respectively (Sato et al.,
2004). These pectins are classified as high-methoxyl pectins
(Glenn, 1953). All the other reagents used were of reagent
grade and were used without further purification.
Measurement of water activity For sugar solutions, wa-
ter activity (Aw) is expected to be described by the following
equation (Kozak et al., 1968):
Aw = (1 – Xs) exp (αXs2) (1)
where XS is the molar fraction of solute and the parameter α
is an experimentally determined constant, which represents
the aqueous solvent-ordering (Miyawaki et al., 1997). The
parameter α for sugars are -1.699, -1.929, -2.734, -7.405,
-8.775, and -9.549 for ribose, mannose, glucose, sucrose,
trehalose, and maltose, respectively (Miyawaki et al., 1997;
Sato et al., 2004).
When pectin coexisted with sugar, the effect of pectin
coexistence on Aw was neglected because of the much lower
molar concentration of pectin compared with sugars so that
the AW value without pectin was employed. Average molecu-
lar weight of pectin is reported to be over 105 daltons using
high-performance size exclusion chromatography (Howard,
1980). However, when the determining the precise effect of
the coexistence of pectin was necessary, AW was measured
by a water activity meter (Aqua Lab CX-3, AINEX, Tokyo,
Japan) at 25℃.
Viscosity measurement for pectin solutions Pectin pow-
der was suspended and dissolved to be 2% in distilled water
containing various concentration of sugars at 50℃. The
sample was kept overnight at 50℃ until use. Then, 7 mL of
the sample solution was poured into the sample cell, and the
apparent viscosity was measured by a rotational viscometer
(B8L, Tokimec, Tokyo, Japan) with rotational speed varying
from 0.5 to 100 rpm. Because of the shear-thinning property
of the pectin solution sample (Marcotte et al., 2001), the ap-
parent viscosity decreased with an increase in the rotational
speed, then stabilized in the rotational speed range typically
higher than 30 rpm (apparent shear rate=39.69 s-1).
For sugar solutions without pectin, the dynamic viscos-
ity was measured by Cannon-Fenske viscometer (Shibata,
Tokyo, Japan) since Newtonian flow is expected in this case.
The viscosity was calculated from the dynamic viscosity and
the density measured by a specific gravity meter (DA-130,
Kyoto Electronics, Kyoto, Japan).
Results and DiscussionActivation energy for viscosity of sugar solutions Figure
1 shows the effect of AW on the viscosity of sugar solutions
at 25℃, ηL, which could be described well by the following
2nd order polynomial of Aw.
ηL = ηW + a (1 – AW) + b (1 – AW)2 (2)
where ηW is the viscosity of pure water, a represents the
Einstein’s volumetric effect of solute and its hydration (Her-
skovits and Kelly, 1973), and b represents the nonlinear term.
Table 1 lists the experimental constants a and b along
with ηW for various sugar solutions at various temperatures,
which show good applicability of Eq. (2) to all the sugar
solutions tested here. From ηW , a, and b in Table 1, the tem-
perature dependence of ηL could be calculated at various
temperatures at fixed Aw, which is expected to be described
by an Arrhenius-type equation (Scott Blair, 1953; Kar and
Arslan, 1999b) as follows:
ηL = η0 exp(Ea/RT) (3)
where η0 is a pre-exponential factor (mPa·s), Ea is the ac-
tivation energy for viscosity (kJ/mol), R is the gas constant
(=8.3145 J/mol/K), and T is the absolute temperature (K).
According to Eq. (3), the logarithm of ηL showed a strong
linear relationship to the inverse of absolute temperature
(1/T ), as shown in Figure 2. From the slope of Figure 2, Ea
was calculated. Results are listed in Table 2 for various sugar
solutions at various Aw. The Ea slightly increased with a de-
crease in Aw and was higher for solutions with disaccharides
than those with monosaccharides.
Intermolecular Interaction of Pectin
0
0.5
1
1.5
2
2.5
0.980.9850.990.9951
SucroseGlucoseRibose
ηL(mPa・
s)
Aw
Fig. 1. Viscosity of sugar solutions at 25℃.
234 Y. Sato et al.
Sugar Temperature (℃) ηW** a b R
Ribose 5 1.521 26.56 835.15 0.997
10 1.307 15.78 849.46 0.997
15 1.135 10.17 1037.70 0.994
20 1.002 12.52 512.99 0.997
25 0.890 13.50 243.20 0.997
30 0.797 10.77 256.19 0.999
35 0.719 10.97 147.93 1.000
40 0.653 9.41 176.23 1.000
Mannose 5 41.80 1012.90 0.997
10 30.66 923.12 0.998
15 23.99 850.67 0.999
20 19.41 731.51 0.998
25 20.60 288.50 0.999
30 17.29 280.91 1.000
35 15.11 245.25 0.999
40 13.91 218.70 0.999
Glucose 5 39.43 1363.80 0.999
10 34.21 862.98 0.999
15 25.68 877.57 0.999
20 28.07 305.98 0.966
25 19.98 480.46 0.999
30 17.86 347.22 0.999
35 15.83 292.65 0.999
40 14.16 263.12 0.999
*)ηL = ηW + a(1-Aw)+ b(1-Aw)2
**)Speight(2005).
Sugar Temperature (℃) ηW a b R
Sucrose 5 61.68 5078.90 0.999
10 53.98 3605.50 1.000
15 45.76 2971.70 1.000
20 38.26 2529.00 1.000
25 33.85 2022.20 1.000
30 29.93 1673.60 0.998
35 26.43 1422.70 0.998
40 24.07 1192.60 0.997
Trehalose 5 46.18 7152.60 0.998
10 37.45 5520.70 0.999
15 35.00 4340.30 0.999
20 29.67 3626.80 0.999
25 26.52 2994.50 0.999
30 24.00 2486.30 0.999
35 21.90 2064.20 0.999
40 25.51 1335.20 0.999
Maltose 5 75.14 4735.60 0.999
10 50.75 4190.00 0.999
15 45.44 3305.40 0.999
20 38.90 2726.40 0.999
25 29.44 2562.40 0.999
30 26.85 2074.90 0.999
35 25.02 1654.00 0.999
40 25.65 1160.60 1.000
*)ηL=ηW + a(1-Aw)+ b(1-Aw)2
Table 1-1. Parameters in Eq. (2)* for viscosity of sugar solution as a function of water activity (monosaccharides).
Table 1-2. Parameters in Eq. (2)* for viscosity of sugar solution as a function of water activity (disaccharides).
-0.5
0
0.5
1
1.5
3.1 3.2 3.3 3.4 3.5 3.6
SucroseGlucoseRiboseWater
lnη
L(-)
1000/T(K-1)
at Aw = 0.985
Fig. 2. Arrhenius plot for viscosity of sugar solutions at Aw = 0.985.
Sugar Aw Ea(kJ/mol) R
No sugar added 1.000 17.5 0.997
Ribose 0.995 17.4 0.999
0.990 17.8 0.999
0.985 18.6 0.999
0.980 19.6 0.998
Mannose 0.995 18.0 0.998
0.990 18.8 0.998
0.985 19.8 0.998
0.980 20.8 0.998
Glucose 0.995 18.0 0.999
0.990 18.8 0.999
0.985 19.8 0.999
0.980 20.7 0.998
Sucrose 0.995 18.3 0.999
0.990 19.7 0.999
0.985 21.0 0.999
0.980 22.1 0.999
Trehalose 0.995 17.8 0.998
0.990 19.5 0.998
0.985 21.3 0.999
0.980 22.9 1.000
Maltose 0.995 18.6 0.998
0.990 20.1 0.998
0.985 21.3 0.999
0.980 22.3 1.000
Table 2. Activation energy for viscosity of sugar solutions.
235
In a sugar solution, there are three different intermolecu-
lar interactions: (1) water-water, (2) water-sugar, and (3)
sugar-sugar. Among these, the sugar-sugar interaction would
be weak for the following reason. For sugar solutions, Aw
was described by Eq. (1), from which the activity coefficient
of water, γW, is calculated to be exp(αXs2). As the parameter α is negative, as reported before (Miyawaki et al., 1997), γW
is less than unity, which suggests that the sugar-sugar inter-
action is negative. If the sugar-sugar interaction is positive, γW should be larger than unity (Kozak et al., 1968; Lilley,
1994). This means that the direct sugar-sugar interaction is
negligible in sugar solutions so that a slight increase in EA
with a decrease in Aw might be attributed to the sugar-water
interaction: hydration of sugar.
Intermolecular interaction among pectin molecules in so-
lutions without sugar Figure 3 shows the effects of temper-
ature and concentration on the viscosity of the citrus pectin
solution, ηH. Also in this case, Eq. (3) was applicable so that
the logarithm of ηH showed linear dependence on 1/T, and
the activation energy of viscosity, Ea, could be determined
from the slope. Ea increased from 17.5 to 31.9 kJ/mol with
an increase in pectin concentration up to 2.0%, as shown in
Figure 4. Kar and Arslan (1999b) reported Ea ranging from
19.6 to 27.2 kJ/mol for the viscosity of orange peel pectin
in concentrations ranging from 0.25 to 2.0%. Marcotte et al.
(2001) obtained Ea for viscosity of pectin ranging from 19.6
to 22.7 kJ/mol in pectin concentrations ranging from 1 to
5%.
Figure 4 also shows that the viscosity of pectin solution
increases exponentially with an increase in pectin concentra-
tion showing corresponding changes in the increase of pec-
tin-pectin interaction. With an increase in pectin concentra-
tion, the effect of water-pectin interaction increases, but this
effect is linearly proportional to the pectin concentration. The
pectin-pectin interaction, however, increases proportionally
to the square of pectin concentration so that an increase in Ea
with an increase in pectin concentration should be attributed
to the increase in the pectin-pectin interaction comprising
hydrogen-bonding and hydrophobic interaction for high-
methoxyl pectins (Oakenfull and Scott, 1984; Crandall and
Wicker, 1986; Oakenfull, 1991). Oakenfull and Scott (1984)
quantitatively evaluated the contributions of the hydrogen-
bonding and hydrophobic interactions to the pectin-pectin
interaction in the gelation process of high-methoxyl pectin.
They reported that the contributions of the hydrogen-bonding
and the hydrophobic interaction are -37.5 and -18.6 kJ/mol,
respectively, both of which are necessary to overcome the
entropy equivalent (+41.1 kJ/mol) for the configuration
change of the pectin molecule.
Intermolecular interaction among pectin molecules in
solutions with sugars Figure 5 shows the effect of the co-
existence of sugars on the viscosity, ηHL, of 2% citrus pectin
solutions. With an increase in sugar concentration, the vis-
cosity of pectin solution drastically increased. The extent
of viscosity increase is also dependent on the type of sugar.
Intermolecular Interaction of Pectin
-1
0
1
2
3
4
5
6
3.1 3.2 3.3 3.4 3.5 3.6
2.0%1.5%1%0.5%0%
lnη
H(-)
1000/T(K-1)
Fig. 3. Arrhenius plot for viscosity of citrus pectin solutions with concentration varied.
Fig. 4. Effect of concentration of citrus pectin on viscosity at 25℃ and activation energy for viscosity.
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5 2
Ea(kJ/mol)η(mPa・s)
Ea(
kJ/mol),
ηH(mPa・
s)
Citrus pectin (%)
236
Sugar with stronger solvent-ordering activity was reported
to more greatly increase the viscosity (Sato and Miyawaki,
2000; Sato et al., 2004).
The dependence of ηHL on AW could be described by the
similar equation with Eq. (2) as follows:
ηHL = ηH + a’(1 – AW) + b’(1 – AW)2 (4)
where ηH, a’, and b’ are experimentally determined con-
stants. Although ηH should be a universal constant, theoreti-
cally, as was the case for ηW in Eq. (2), the actual value of ηH
was slightly different among experiments. Table 3 lists these
constants for 2% citrus pectin solutions with various sugars
at various concentrations with varied temperature, showing
good applicability of Eq. (4) with good correlation coeffi-
cients. For ηHL, Eq. (3) was also applicable so that the loga-
rithm of ηHL was plotted against 1/T in Figure 6 (AW = 0.985),
showing a good linear relationship. From the slope of this
plot, Ea was obtained and listed in Table 4 for 2% solutions
of citrus and apple pectin with various sugars at various AW.
From Table 4, Ea for viscosity of 2% citrus and apple
pectin solutions without sugar are 31.9 and 27.4 kJ/mol, re-
spectively. These values are much higher than that for pure
water (17.5 kJ/mol) because of the pectin-pectin interaction,
which has higher activation energy than water-water interac-
tion, as described previously. When sugars coexist, the acti-
vation energy for the viscosity of pectin solutions increased
more for an increase in sugar concentration. This increase
in Ea was dependent both on the AW and the type of sugars.
When compared at the same AW, Ea was much higher for di-
saccharide solutions than those of monosaccharide.
Y. Sato et al.
0
50
100
150
200
250
300
0.980.9850.990.9951
SucroseGlucoseRibose
ηHL(mPa・
s)
Aw
Fig. 5. Effect of coexistence of sugars on viscosity of citrus pectin solutions.
Sugar Temperature(℃) ηH
Ribose 5 213.84 10834 16121 0.999
10 166.03 5698 38350 0.999
15 125.52 4119 17313 0.997
20 101.62 2431 29134 0.993
25 75.16 3124 -31106 0.999
30 65.51 1798 -14161 0.980
35 55.72 1047 14671 0.990
40 45.61 1383 -16489 0.981
Mannose 5 230.07 16097 -33471 0.993
10 164.01 10293 27667 0.995
15 124.77 7333 -13837 0.993
20 98.79 4969 8520 0.995
25 78.63 4786 -60649 0.989
30 66.97 2568 5883 0.995
35 55.31 2381 -20072 0.984
40 49.00 918 47099 0.987
Glucose 5 218.35 11832 672060 0.993
10 154.98 12964 -26088 0.996
15 120.56 7172 94272 0.998
20 94.54 4989 100200 0.998
25 75.36 4665 -1343 0.995
30 61.79 4027 -20526 0.998
35 54.34 2212 21554 0.995
40 49.04 1310 35090 0.999
*)ηHL =ηH + a’(1-Aw) + b’(1-Aw)2
Rb’a’
Sugar Temperature (℃) ηH
Sucrose 5 210.00 53056 -2314800 1.000
10 150.00 36614 -1721500 1.000
15 124.08 9198 913700 0.993
20 92.68 11413 264830 0.990
25 73.43 8989 141430 0.994
30 67.10 6028 121910 0.994
35 61.64 3262 148300 0.988
40 55.32 3510 37613 0.953
Trehalose 10 152.70 26601 272980 1.000
15 119.84 15973 455290 1.000
20 103.24 -357 1617100 0.994
25 74.73 7347 520370 0.997
30 63.22 4946 429350 0.998
35 54.37 2747 373450 0.997
40 48.69 2694 223910 0.998
Maltose 5 196.70 53005 -2216000 1.000
10 161.84 19509 638370 0.997
15 124.67 5888 1275500 0.993
20 96.96 4835 831020 0.993
25 79.87 2751 675310 0.997
30 65.27 1938 509310 0.998
35 56.00 1468 387500 0.996
40 49.66 1123 274810 0.997
*)ηHL =ηH + a’(1-Aw) + b’(1-Aw)2
Rb’a’
Table 3-1. Parameters in Eq. (4)* for viscosity of 2% citrus pectin solutions with sugars as a function of water activity (monosaccha-rides).
Table 3-2. Parameters in Eq. (4)* for viscosity of 2% citrus pectin solutions with sugars as a function of water activity (disaccharides).
237
In the aqueous pectin solution with sugar, six intermo-
lecular interactions are expected to exist: (1) water-water,
(2) water-sugar, (3) sugar-sugar, (4) water-pectin, (5) sugar-
pectin, and (6) pectin-pectin. The activation energy for the
former two was small, as shown in Table 2, and the contribu-
tion of sugar-sugar interaction would not be as important as
previously discussed. Therefore, the latter three interactions
will be considered here.
In pectin solutions, the pectin-pectin interaction is more
important than water-pectin interaction when the pectin con-
centration is high as was described before. As for the effect
of sugars, Chen and Joslyn (1967) explained the viscosity-
enhancing property of sugar by the dehydration and the
hydrogen-bonding-formation activity that enhances the ag-
gregation among pectin molecules. Kar and Arsln (1999a)
attributed the viscosity-enhancing effect of sugars to the de-
crease in dielectric constant, dehydration action, and hydro-
gen bonding formation. Bulone et al. (2002) investigated the
role of sucrose in pectin gelation by static and dynamic light
scattering and reported that the apparent gyration radius of
the pectin molecule slightly increased with sucrose concen-
tration. Fishman et al. (2004) applied atomic force micros-
copy to observe nanostructure of native pectin sugar acid gel
and concluded that sugars strongly adsorb on pectin with the
ratio of bound sugar to pectin in excess of 100 to 1 (w/w).
We tried to measure the sugar-pectin interaction directly
by the measurement and comparison of AW of sugar solu-
tion with and without pectin. The AW values for 30% sucrose
solutions without and with 2% citrus pectin were 0.975 and
0.971, respectively. This insignificant difference between
the two strongly suggests that the direct interaction between
sugar and pectin is weak. In other cases, AW of sugar solution
should increase with the coexistence of pectin due to the de-
crease in the number of sugar molecules through the adsorp-
tion on pectin (Fishman et al., 2004) if a strong sugar-pectin
interaction exists (Kozak et al., 1968; Lilley, 1994).
Thus the rapid increase in viscosity of pectin solution
with the addition of sugars in Figure 5 is ascribed to the
increase in pectin-pectin interaction, which has higher acti-
vation energy than the other interactions. This explains the
increase in Ea for the viscosity of pectin solutions with an in-
crease in sugar concentration in Table 4. When sugars coex-
ist, sugars are strongly competitive in hydration with pectin
molecules so that the amount of hydration of pectin will be
reduced to increase the pectin-pectin interaction, which is re-
sponsible for the increase in Ea with a decrease in AW shown
in Table 4. This trend is, as shown in Figure 7, more obvious
for disaccharides than for monosaccharides because of the
higher solvent-ordering activity for the former.
As was reported by Oakenfull and Scott (1984), pectin-
pectin interaction comprises hydrogen bonding and hydro-
phobic interaction. For comparison at the same Aw, the ef-
fect of hydrogen bonding would be similar among different
sugars so that different effects on pectin-pectin interactions
among sugars should be responsible for the different effects
Intermolecular Interaction of Pectin
3.5
4
4.5
5
5.5
6
6.5
3.1 3.2 3.3 3.4 3.5 3.6
SucroseGlucoseRiboseWater
lnη
HL(-)
1000/T(K-1)
at Aw = 0.985
Fig. 6. Arrhenius plot for 2% citrus pectin solutions with various sugars at Aw = 0.985.
Sugar Citrus pectin Apple pectin
Aw Ea (kJ/mol) R Ea (kJ/mol) R
No sugar added 1.000 31.9 0.998 27.4 0.999
Ribose 0.995 33.8 0.997 29.8 0.998 0.990 35.5 0.996 31.7 0.999
0.985 37.0 0.996 32.4 0.999
0.980 38.5 0.996 31.3 0.999
Mannose 0.995 35.2 0.997 30.7 0.999
0.990 37.1 0.997 32.0 0.999
0.985 38.2 0.997 32.2 0.999
0.980 38.9 0.995 32.8 0.999
Glucose 0.995 34.2 0.997 30.8 0.997
0.990 37.1 0.997 32.2 0.999
0.985 36.8 0.999 31.9 1.000
0.980 37.2 0.997 32.0 0.999
Sucrose 0.995 35.9 0.990 35.8 0.992
0.990 36.2 0.998 33.2 0.999
0.985 41.4 0.998 33.2 0.999
0.980 45.5 0.995 36.1 1.000
Trehalose 0.995 35.7 0.992 35.7 0.999
0.990 36.9 0.999 32.1 0.998
0.985 44.5 0.995 33.4 0.999
0.980 41.1 1.000 34.5 1.000
Maltose 0.995 38.6 0.992 32.7 0.998
0.990 38.5 0.999 31.7 1.000
0.985 40.2 0.999 33.3 1.000
0.980 41.1 1.000 34.0 1.000
Table 4. Activation energy for viscosity for 2% pectin solutions with various sugars.
238
on the hydrophobic interaction through differences in the
solvent-ordering activity (Sato et al., 2004).
Acknowledgements We thank Ms. Takenaka, Ms. Koike, Ms. Hino,
and Ms. Takagi for their technical assistance. This study was partly
supported by a Grant-in-Aid for Scientific Research from Japan So-
ciety for the Promotion of Science (No. 14580144).
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Y. Sato et al.
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35
40
45
-9-7-5-3-1
Citrus pectinApple pectin
Ea(kJ/mol)
Parameter α
R = 0.830
R = 0.931
at Aw = 0.985
Fig. 7. Correlation between the parameter α and the activa-tion energy for viscosity at Aw = 0.985.