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Treball presentat
European Drying Conference –EuroDrying’2011
Palma. Balearic Island, Spain, 26-28 0ctobre 2011
MOISTURE DESORPTION ISOTHERMS, ISOSTERIC HEATS OF DESORPTION
AND GLASS TRANSITION OF FRESH PEAR AND APPLE:
EXPERIMENTAL AND MATHEMATICAL INVESTIGATION
DJENDOUBI MRAD Nadia (1, 2, 3), BONAZZI Catherine (1, 3), COURTOIS Francis (1),
BOUDHRIOUA Nourhène (4), KECHAOU Nabil (1)
(1)
Groupe de Recherche en Génie des Procédés Agroalimentaires Unité de Recherche : Mécanique des Fluides Appliquée et
Modélisation Ecole Nationale d’Ingénieurs de Sfax BP 1173, 3038, Sfax, Université de Sfax, TUNISIE
(2)
AgroParisTech, UMR 1145 Génie Industriel Alimentaire, 1 avenue des Olympiades F-91300 Massy
(3)
INRA, UMR 1145 Génie Industriel Alimentaire, 1 avenue des Olympiades F-91300 Massy
(4)
Institut Supérieur de Biotechnologie, Sidi Thabet, Tunis, Université de la Mannouba, Tunisie.
Abstract
Moisture desorption isotherms of apples and pears were determined at 30°C, 45°C and 60°C using the standard staticgravimetric method. These desorption isotherms decreased with increasing temperature, exhibited type III behavior according
to BET classification. The experimental data were adequately fitted using six models. The Peleg model best fitted the whole
set of data over the range of investigated temperatures and water activities (0.996 ≤ R² ≤ 0.999 and 0.004 ≤ S ≤ 0.011).
Thermal transitions of the both fruits were analyzed by using Differential Scanning Calorimetry. Glass transition temperature
of both samples decreased linearly with the increase of water activity.
Keywords: apple, pear, glass transition, water activity, desorption isotherm.
INTRODUCTION
Equilibrium experiments
Glass transition Temperature (Tg) is a powerful tool
for understanding the quantification of water
mobility in foods and controlling the shelf-life of
products. As aw has been proved inadequate for some
food products shelf-life evaluation, Tg has an
advantage over aw (Delgado & Sun, 2002). At
temperatures below Tg, any food product has been
considered to be stable. However, the concept of
glass transition cannot predict the microbial stability
of foods with confidence and it needs further
research to understand the influence of water and
solute mobility for controlling growth and metabolic
activity of micro-organisms in foods (Le Meste et al.,
2002). Therefore, Tg, moisture content and aw are
complimentary to each other to quantify the water
migration pattern in food precisely.
Desorption isotherms of fresh apple and pear samples
were carried out by using the standard static
gravimetric method (Wolf et al., 1985). Various
water activities (aw) ranged between 0.07 to 0.98
were selected using several saturated salt solutions
and three temperatures (30, 45 and 60°C).
When equilibrium was reached, the equilibrium
moisture contents (X (d.b.)) of samples were
determined from values of initial moisture content
and from final weights of the samples. The moisture
content was measured by using oven drying at 70°C
for 24 h (AOAC, 1984).
Glass transition temperature
Tg of samples conditioned at different moisture
contents was determined by using the Differential
Scanning Calorimetry (DSC) (DSC-Q100, TA,
USA). The instrument was calibrated by using
indium standard. A 12 - 18 mg sample was placed
into a DSC pan, and hermetically sealed. An empty
pan was used as reference (air). The sample was
scanned from -80 to 100°C at a rate of 10 °C/min to
determine its thermal behavior. Tg was recorded as
the middle temperature in curves of the heat flow
versus temperature.
This investigation was undertaken in order to study
the water desorption isotherm of fresh apples and
pears at 30, 45 and 60°C, to propose a mathematical
model for prediction of their desorption, to evaluate
the constants of desorption models, to calculate the
net isosteric heat of desorption from the experimental
data and to determine the Tg of those samples as a
function of aw.
MATERIAL AND METHODS
Material
Fitting equations
Golden Delicious apples, Pyrus communis cv.
Conference pears purchased at a local store. Fruits
were peeled and cut into small pieces of 10 mm long,
0.8 cm wide and 0.8 cm thick.
The experimental desorption data of all samples at
three temperatures was fitted to six sorption
equations: GAB, BET, Halsey, Modified Halsey,
Oswin and Peleg (Djendoubi et al., 2009).
1 European Drying Conference –EuroDrying’2011
Palma. Balearic Island, Spain, 26-28 0ctobre 2011
RESULTS AND DISCUSSION
Water plasticization behaviour
The Gordon and Taylor model (1952) has proved to
be a reliable predictor of glass transition temperatures
of sugars at various water contents .It has been used
in several fruit samples. Another relationship of
interest in the prediction of the physical state in food
materials (Tg as a function of water activity) is given
by Khalloufi et al. (2000) and Roos (1987). In this
study, only Roos model (1987) was used.
The experimental results for the equilibrium moisture
content of apples and pears at each aw for three
different temperatures are given in Fig.1.
1.4
(1)
where A and B are Roos model parameters.
i =1
S=
eq i
− X eq cali
1.4
(2)
r = 1−
∑ (X
nexp. data
eq
i =1
p=
100
nexp.data
nexp.data
∑
− X eqi
)
2
)
Xeqi
i=1
(3)
X eq i
(4)
eq i
(5)
Calculation of the isosteric heat of desorption
The net isosteric heat of desorption qst, n (kJ / mol)
was calculated from the experimental desorption
isotherms by using the Clausius – Clapeyron
equation (Labuza et al., 1985);
ln(aw ) = −
qst, n
R
×
1
+ Cst
T
0.8
1
It is widely accepted that an increase in temperature
results in a decreased equilibrium moisture content.
For apple and pear, our results were in agreement
with the above statement. For apples and pears with
(6)
where R is the universal gas constant (kJ / mol.K)
and T the desorption isotherm temperature (K).
2 0.6
The desorption isotherms of studied fruits showed
type III behaviour, according to the BET
classification (Iglesias & Chirife, 1982). The
desorption isotherms were not sigmoid and in
agreement with the reported sharp for high sugar
foodstuffs. As it can be seen all isotherms were very
similar in shape, showing a gradually increasing
sorption pattern, which is characteristic of fruits that
have a significant sugar content. At low water
activities the products sorbed relatively small
amounts of water, and as aw increased the desorption
increases considerably. At low aw the desorption is
mainly a superficial phenomenon due to the
biopolymers and crystalline sugars, whereas at high
aw the increase in desorption is mainly due to the
dissolution of sugars (López-Maloet al., 1997). A
similar behaviour has been reported by other authors
for different fruits such as pineapple (Telis & Sobral,
2001), persimmon (Sobral et al., 2001), strawberry
(Moraga et al., 2004), guava, mango and pineapple
(Hubinger et al., 1992).
nexp . data
i =1
0.4
Figure 1. Desorption isotherms obtained at 30, 45
and 60°C for apple (a) and for pear (b).
by using this relation:
∑X
0.2
Water activity(-)
is number of experimental data. X eq was calculated
nexp .data
(b)
0.6
0
is experimental moisture content,
1
0.8
1
0
n param is number of model's parameters and nexp .data
X eq =
1
0.8
0.2
Where X eq cali is moisture content calculated by the
model,
0.4
0.6
Water activity (-)
0.4
2
Xeqcali − Xeqi
0.2
30°C
Peleg_30°C
45°C
Peleg_45°C
60°C
Peleg_60°C
1.2
− X eq cali
eqi
0
2
nexp.data
i =1
0.6
0
)
nexp .data − n param
∑ (X
0.8
(a)
0.2
X (g H2O/g d.b.)
∑ (X
1
0.4
The adequacy of each model was evaluated by
standard error coefficient, correlation coefficient and
p-value calculated by software Curve Expert 3.1®
(Djendoubi et al., 2009).
nexp . data
30°C
Peleg_30°C
45°C
Peleg_45°C
60°C
Peleg_60°C
1.2
X (g H2O/g d.b.)
Tg = Aaw + B
Desorption isotherms
European Drying Conference –EuroDrying’2011
Palma. Balearic Island, Spain, 26-28 0ctobre 2011
value tends to zero, the influence of adsorbent on the
adsorbed molecules becomes negligible.
high pectin and sugar contents, there was no
intersection point with increase in temperature as
reported earlier by Roman et al. (1982) for apple.
The heat of desorption of pear is greater than that of
apple at low moisture contents. This indicates that the
energy required in the desorption process of pear is
greater than in the desorption process of apple.
Different equations proposed in the literature were
used to fit desorption data. The best fit was obtained
with the Peleg model which describes the
experimental data with p-value less than 14%,
followed by the models of GAB, BET, Oswin,
Modified Halsey and Halsey (data not shown).Table
2 shows the peleg parameter values and the mean
relative deviation obtained, the correlation coefficient
of the of nonlinear regression analysis were higher
than 0.99.
Glass transition
Thermogram obtained by DSC analysis of
equilibrated samples for fresh apples stabilized at
different levels of aw are shown in Fig. 3.
Pear
Apple
Table 2. Estimated parameters of the Peleg model
used for describing desorption isotherms of apples
and pears and the corresponding statistical
parameters.
T
(°C)
30
45
60
30
45
60
A
3.680
0.094
0.609
0.315
3.163
0.144
Parameters
B
C
8.878 0.170
0.326 3.592
2.868 66.20
0.218 3.818
6.026 0.084
0.136 3.842
P (%)
S
D
0.235
8.522
27.57
6.561
0.024
7.642
0.042
0.006
0.033
0.049
0.071
0.023
r
12.50 0.999
5.75 0.999
10.10 0.990
13.20 0.999
14.75 0.998
8.95 0.999
Figure 3. Typical DSC scans of apple
equilibrated under different aw.
This figure presents only portion of thermogram
around the glass transition temperature for different
water activities. Similar curves were obtained for the
fresh pears equilibrated at different water activities.
Heat of desorption
The values of the isosteric heat of desorption, qst,n,
were calculated from the equilibrium data at different
temperature using Eq. (6) and obtained at different
moisture contents. The variation of the heats of
desorption of the products with moisture content is
shown in Fig.2.
Tg of apples and pears are shown in Fig 4.
40
30°C
60°C
Tg (°C)
-20
100
-40
90
-60
-80
70
Apple
Pear
60
0
0.2
0.4
0.6
0.8
1
Water activity (-)
50
40
40
20
30
0
20
-20
30°C
Tg (°C)
qst,n (kJ/mol)
45°C
0
80
10
(b)
45°C
60°C
-40
-60
0
0
0.5
1
1.5
2
2.5
3
3.5
4
X (kg H2O/kg d.b.)
Figure 2. Variation of the isosteric heat of desorption
versus equilibrium moisture content. -80
-100
0
0.2
0.4
0.6
0.8
Water activity (-)
Figure 4. Tg-aw relationship for apples (a) and pears
(b). Experimental points and fited Roos models
(lines).
As seen in Fig.2, isosteric heats of desorption are
high at low moisture contents (<10%). In fruits, the
net isosteric heat of desorption decreased gradually
(up to 15-25 kg/100 kg dry solids), approaching zero
at moisture content of 25-40 kg/100 kg dry solids.
According to Iglesias & Chirife (1976), as the qst,n
The magnitudes of Tg decreased with an increase in
water activity resulting in a maximum glass transition
temperature at the lowest water activity. There are no
3 (a)
20
European Drying Conference –EuroDrying’2011
Palma. Balearic Island, Spain, 26-28 0ctobre 2011
guava, mango and pineapple. Journal of Food
Science, 57(6), 1405-1407.
differences in Tg values for apple equilibrated at
60 and 45°C at water activities less than 0.10. This
result support desorption isotherm results of fresh
apple at 45 and 60°C, where for water activities less
than 0.10 no differences are noted.
Hubinger, M., Menegalli, F.C., Aguerre, R.J., Suarez,
C., 1992. Water vapor absorption isotherms of guava,
mango and pineapple. Journal of Food Science, 57,
1405–1407.
CONCLUSION
Iglesias, H. A., & Chirife, J. (1976). Isosteric heats of
water vapor sorption on dehydrated foods. Part I:
Analysis of the differential heat curves.
Lebensmittel-Wissenschaft und Technologie, 9, 116–
122.
The moisture desorption isotherms of apple and pears
at different temperatures and water activities were
determined with the standard gravimetric method
using various saturated salt solutions. The
equilibrium moisture content increased with
decreasing temperature at constant moisture water
activity.
Iglesias, H. A., & Chirife, J. (1982). Handbook of
food isotherms (pp. 170–175). New York: Academic
Press.
Among the sorption models tested, the Peleg
equation describes the desorption data well over the
range of temperatures and water activities studied.
Khalloufi, S., El-Maslouhi, Y., & Ratti, C. (2000).
Mathematical model for prediction of glass transition
temperature of fruit powders. Journal of Food
Science, 65, 842–845.
The net isosteric heat of desorption can be calculated
using the Clausius-Clapeyron equation. The heats of
desorption increased with decreasing moisture
content.
Moraga, G., Martínez-Navarrete, N., & Chiralt, A.
(2004). Water sorption isotherms and glass transition
in strawberries: influence of pretreatment”. Journal of
Food Engineering, 62, 315-321.
Glass transition temperatures of saturated salt
equilibrated samples were determined. Tg decreased
with an increase in water activity resulting in a
maximum glass transition temperature at the lowest
water activity. For both fruits equilibrated at 30,
45 and 60°C, differences in Tg was observed. But no
differences is noticed for apple equilibrated at
45 and 60°C with water activities less than 0.10.
Roman, G. N., Urbician, M. J., & Rotstein, E. (1982).
Moisture equilibrium in apples at several
temperatures: Experimental data and theoretical
considerations. Journal of Food Science, 47, 1484–
1488, 1507.
Sobral, P. J. A., Telis, V. R. N., Habitante, A. M. Q.
B., & Sereno, A. (2001). Phase diagram for freezedried persimmon. Thermochimica Acta, 376, 83-89.
ACKNOWLEDGEMENTS
This work was funded by the « Ministère de
l’Enseignement Supérieur, de la Recherche
Scientifique et de la Technologie, Tunisie » and the
« Gouvernement français».
Telis, V.R.N., Sobral, P.J.A., 2001. Glass transitions
and state diagram for freeze dried pineapple.
Lebensmittel-Wissenschaft und-Technologie-Food
Science and Technology 34, 199–205.
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