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Water sorption isotherms of starch powders
Journal of Food Engineering 61 (2004) 297–307 www.elsevier.com/locate/jfoodeng
Water sorption isotherms of starch powders Part 1: mathematical description of experimental data A.H. Al-Muhtaseb, W.A.M. McMinn, T.R.A. Magee
*
Food Process Engineering Research Group, School of Chemical Engineering, QueenÕs University Belfast, David Keir Building Stranmillis Road, Belfast, BT9 5AG, UK Received 20 January 2003; accepted 13 April 2003
Abstract Adsorption and desorption isotherms for potato, highly amylopectin and highly amylose starch powders were determined at 30, 45 and 60 C using a gravimetric technique. Samples were equilibrated in desiccators containing sulphuric acid solutions of known water activity (0.05–0.95), and placed in temperature-controlled cabinets for approximately three weeks. The starch powders exhibited Type II behaviour. The sorption capacity decreased with increasing temperature. The data obtained were fitted to several models including two parameter relationships (Halsey, Oswin, Henderson, Modified-BET and Smith), three parameter equations (GAB, Ferro-Fontan) and four parameter equation (Peleg). A non-linear least square regression program was used to evaluate the models constants. The empirical Peleg model followed by the kinetic GAB and the semi empirical Ferro-Fontan models were found to best represent the experimental data in the water activity range 0.05–0.95. In the range of water activity 0.35–0.95 the Smith model was shown to give the closest fit to the experimental data. 2003 Elsevier Ltd. All rights reserved. Keywords: Sorption isotherm; Potato starch; Highly amylopectin starch; Highly amylose starch; Mathematical models; Hysteresis
1. Introduction Control of moisture content during the processing of foods is an ancient method of preservation, and probably humankindÕs first ‘‘technology’’ for extending the stability of foods. This is achieved by either removing, or binding water such that the food becomes stable to both microbial and chemical deterioration (Labuza, 1980). The most common limitation on the shelf life of food is microbial growth, hence several preservation processes are aimed at achieving stability of foods by reducing the moisture content to levels below those required by micro-organisms for survival and reproduction (Aguilera & Stanley, 1999). Sorption characteristics have, and are currently being examined in light of their influence on the storage stability of dehydrated products, as well as their affect on the diffusion of water vapour.
*
Corresponding author. Tel.: +44-(0)28-9027-4255; fax: +44-(0)289038-1753. E-mail address: [email protected] (T.R.A. Magee). 0260-8774/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0260-8774(03)00133-X
In 1957, Scott termed the equilibrium relative humidity, i.e. availability of water in food, water activity (Scott, 1957). The work was widely acclaimed and led to a rapid expansion in the use of water activity, denoted (aw ), which is now one of the major control variables in food preservation technology (Van den Berg & Bruin, 1981). Water activity is a term indicating the ‘‘quality’’ of the water content of food. It describes the degree of ‘‘boundness’’ of water and, hence its availability to participate in physical, chemical, and microbiological reactions. The relationship between the total moisture content and water activity of the food, over a range of values, at a constant temperature and under equilibrium conditions, yields a moisture sorption isotherm when expressed graphically. This isotherm curve can be obtained in one of two ways; adsorption or desorption. The adsorption and desorption processes are not fully reversible, therefore a distinction can be made between the isotherms by determining whether the moisture levels within the product are increasing or decreasing. The effect of temperature on the sorption isotherm is of great importance given that foods are exposed to a
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Nomenclature A aw B C c0 E DHc DHk
K k0
constant (dimensionless) water activity constant (dimensionless) GAB model parameter (dimensionless) constant (adjusted to the temperature effect) (dimensionless) mean relative percentage deviation modulus (%) difference in enthalpy between mono-layer and multi-layer sorption (J mol1 ) difference between the heat of condensation of water and the heat of sorption of the multilayer (J mol1 ) GAB model parameter (dimensionless) constant (adjusted to the temperature effect) (dimensionless)
range of temperatures during storage and processing, and water activity changes with temperature. Temperature affects the mobility of the water molecules, and the dynamic equilibrium between the vapour and adsorbed phases. In the field of water vapour sorption by a solid sorbent, moisture sorption hysteresis is the phenomena by which two different paths exist between the adsorption and desorption isotherms (Kapsalis, 1981). The effect of hysteresis on food is important, even though it can be relatively low in magnitude. Rizvi (1995) stated that the extent of hysteresis is related to the nature and state of the components in a food. It may reflect their structural and conformational rearrangement, which alters the accessibility of energetically favourable polar sites and thus, may hinder the movement of moisture. Iglesias and Chirife (1976) recognized that it is not possible to give a single explanation of the hysteresis phenomena in foods, due to food being a complex combination of various constituents, which can, not only sorb water independently but also, interact among themselves. Water sorption isotherm equations are useful for predicting water sorption properties of foods, although they provide little insight into the interaction of water and food components (Leung, 1983). Although several mathematical models exist to describe water sorption isotherms of food materials (Iglesias, Chirife, & Lombardi, 1975), no one equation gives accurate results throughout the whole range of water activities, or for all types of foods. Labuza (1975) attributed this to the fact that the water is associated with the food matrix by different mechanisms in different water activity regions. Models available in the literature to describe moisture sorption isotherm can be divided into several categories;
K1 , K2 mi mpi N n 1 , n2 R r T X X0 a c h
equation parameters (dimensionless) experimental value predicted value number of experimental data equation parameters (dimensionless) universal gas constant (8.314 J mol1 K1 ) equation parameter (dimensionless) temperature (K) equilibrium moisture content (kg kg1 dry solid) mono-layer moisture content (kg kg1 dry solid) equation parameter (dimensionless) equation parameter (dimensionless) equation parameter (dimensionless)
kinetic models based on a mono-layer (Mod-BET model), kinetic models based on a multi-layer and condensed film (GAB model), semi-empirical (FerroFontan, Henderson and Halsey models) and empirical models (Smith and Oswin models). The BET model represents a fundamental milestone in the interpretation of multi-layer sorption isotherms, particularly Types II and III (Timmermann, 1989). Many researchers modified the BET model and the modified equation gave a good fit up to water activity 0.9 (Aguerre, Suarez, & Viollaz, 1989). The GAB model is considered to be the most versatile sorption model available in the literature and has been adopted by a group of West European food researchers COST 90 (Bizot, 1983; Van den Berg & Bruin, 1981). Chirife, Bouquet, Ferro-Fontan, and Iglesias (1983) proposed the Ferro-Fontan model. Iglesias and Chirife (1995) reported that the Ferro-Fontan equation accurately represented the sorption isotherm of 92 different food products. Peleg (1993) proposed a fourparameter model and noted that the model can be used for both sigmoidal and non-sigmoidal isotherms, and that it fitted as well as, or better than, the GAB model. The Smith model (1947) is useful in describing the sorption isotherm of biological materials such as starch and cellulose. Henderson (1952) proposed a semi-empirical model for the equilibrium moisture content of cereal grains. Chirife and Iglesias (1978) found that Halsey and Oswin models are also versatile. The objectives of this study were to provide reliable experimental data for the sorption characteristics of starch powders (potato, highly amylopectin, highly amylose) to model the sorption isotherms using selected equations, determine their dependence on temperature, and examine the hysteresis phenomena.
A.H. Al-Muhtaseb et al. / Journal of Food Engineering 61 (2004) 297–307
2. Materials and methods 2.1. Experimental procedure The equilibrium moisture contents of potato (80% amylopectin, 20% amylose) (Roquette, UK), highly amylopectin (99.2% amylopectin, 0.8% amylose) and highly amylose (30% amylopectin, 70% amylose) (National Starch and Chemicals, UK) starch powders were determined by a gravimetric technique, in which the weight was monitored discontinuously within a standard static system of thermally stabilized desiccators. This method was recommended by the COST 90 project (Wolf, Spiess, & Jung, 1985). For adsorption a 6 ± 0.001 g sample of the bone dry powder was placed in a petri-dish inside a dessicator. For desorption, a 12 ± 0.001 g sample of 1 kg kg1 dry basis powder was used. Each experiment was carried out in triplicate. Sulphuric acid (Fisher Scientific, UK) solutions were used to maintain the specified relative humidity inside the desiccators. The effect of temperature and acid concentration on the equilibrium relative humidity val-
Table 1 Water activity of sulphuric acid solutions at selected concentrations and temperatures H2 SO4 solution % (v/v) 5 20 30 40 50 60 70 80
Water activity (aw ) 30 C
45 C
60 C
0.9808 0.8814 0.7549 0.5711 0.3574 0.1677 0.047 0.0059
0.9812 0.8839 0.7629 0.5866 0.3765 0.1834 0.0548 0.0077
0.9818 0.8882 0.7711 0.5989 0.3936 0.1988 0.0611 0.0103
299
ues of sulphuric acid solutions are presented in Table 1 (Ruegg, 1980). The prepared dessicators were then placed in temperature-controlled cabinets maintained at 30, 45 and 60 ± 1 C. The samples were allowed to equilibrate until there was no discernible weight change, as evidenced by constant weight values (±0.001 g). This involved a period of approximately three weeks for potato starch powder and two weeks for highly amylopectin and highly amylose powders. The total time required for removal, weighing and replacing the samples in the desiccators was approximately 30 s. This minimized the degree of atmospheric moisture sorption during weighing. Each experiment was carried out in triplicate. The bone dry mass was determined gravimetrically by drying in a convectional oven at 105 C for 8–10 h (AOAC, 1980).
2.2. Data analysis The isotherm models used to fit the data are presented in Table 2. A non-linear least square regression analysis was used to evaluate the model parameters. To evaluate the goodness of fit of each model, the mean relative percentage deviation modulus ðEÞ was used, which is defined by
E¼
N 100 X jmi mpi j N i¼1 mi
ð11Þ
where mi is the experimental value, mpi is the predicted value, and N is the number of experimental data. The mean relative percentage deviation modulus ðEÞ is widely adopted throughout the literature, with a modulus value below 10% indicative of a good fit for practical purposes (Lomauro, Bakshi, & Labuza, 1985).
Table 2 Isotherm equations for experimental data fitting Model
Mathematical expression
Mod-BET (Aguerre et al., 1989)
X ¼ X0 Caw =½ð1 aw Þð1 C lnð1 aw ÞÞ
ð1Þ
Halsey (Halsey, 1948)
X ¼ ½A=ðT ln aw Þ1=B
ð2Þ
Smith (Smith, 1947)
X ¼ A þ ðB logð1 aw ÞÞ
ð3Þ
Henderson (Henderson, 1952)
X ¼ ½ lnð1 aw Þ=A
Oswin (Oswin, 1946)
X ¼ Aðaw =ð1 aw ÞÞB
Ferro-Fontan (Ferro-Fontan, Chirife, Sancho, & Iglesias, 1982) Guggenheim–Anderson–de Boer (Van den Berg & Bruin, 1981)
Peleg (Peleg, 1993)
1=B
1=r
X ¼ ½c= lnða=aw Þ
ð4Þ ð5Þ ð6Þ
X ¼ X0 CKaw =½ð1 Kaw Þð1 Kaw þ CKaw Þ
ð7Þ
C ¼ c0 expðDHC =RT Þ
ð8Þ
K ¼ k0 expðDHK =RT Þ
ð9Þ
X ¼
K1 anw1
þ
K2 anw2
ð10Þ
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3. Results and discussion 3.1. Desorption and adsorption isotherms The adsorption and desorption isotherms for potato, highly amylopectin and highly amylose starch powders at 30, 45 and 60 C are shown in Figs. 1–6. The equilibrium moisture content at each water activity repre-
Moisture Content (kgkg -1 DS)
Moisture Content (kgkg -1 DS)
0.4
0.3
0.2
0.1
0.0 0.2
0.4 0.6 Water Activity 60°C
45°C
0.8
1.0
0.3
0.2
0.1
0.0
0.2
30°C
0.4 0.6 Water Activity 60°C
Fig. 1. Experimental adsorption isotherms for potato starch powder. DS ¼ dry basis.
45°C
0.8
1.0
30°C
Fig. 4. Experimental desorption isotherms for highly amylopectin powder.
0.4
0.4
-1
Moisture Content (kgkg DS)
Moisture Content (kgkg -1 DS)
0.4
0.0
0.0
0.3
0.2
0.1
0.0
0.3
0.2
0.1
0.0
0.0
0.2
0.4 0.6 Water Activity 60°C
45°C
0.8
1.0
0.0
0.2
30°C 30°C
0.4 0.6 Water Activtiy 60°C
Fig. 2. Experimental desorption isotherms for potato starch powder.
45°C
0.8
1.0
30°C
Fig. 5. Experimental adsorption isotherms for highly amylose powder.
0.4
0.4
Moisture Content (kgkg DS)
0.3
-1
Moisture Content (kgkg -1 DS)
sents the mean value of three replications. Without exception, the adsorption and desorption isotherms demonstrate an increase in equilibrium moisture content with increasing water activity, at a constant temperature. This behaviour is manifested in the form of a sigmoidal shaped curve, thus reflecting a Type II isotherm (according to BrunauerÕs classification) (Brunauer, Deming, Deming, & Troller, 1940). This is in
0.2 0.1 0.0 0.0
0.2
0.4 0.6 Water Activity 60°C
45°C
0.8
1.0
0.3
0.2
0.1
0.0 0.0
0.2
0.4 0.6 Water Activity
30°C 60°C
Fig. 3. Experimental adsorption isotherms for highly amylopectin powder.
45°C
0.8
1.0
30°C
Fig. 6. Experimental desorption isotherms for highly amylose powder.
A.H. Al-Muhtaseb et al. / Journal of Food Engineering 61 (2004) 297–307
than the highly amylopectin and highly amylose powders, particularly in the high water activity range aw > 0:85. In general, the effect of temperature on desorption is more noticeable; an exception to this behaviour was found in the case of potato starch powder at aw > 0:90. The temperature shifts observed have an important practical affect on the chemical and microbiological reactions which cause quality deterioration. An increase in temperature causes an increase in the water activity, at the same moisture content, which in turn causes an increase in the reaction rates leading to quality deterioration (Van den Berg & Bruin, 1981).
3.2. Moisture sorption hysteresis
Moisture Content (kgkg -1 DS)
Figs. 7–9 show the sorption isotherms obtained at 45 C for potato, highly amylopectin and highly amylose starch powders, respectively. The graphs clearly show that the equilibrium moisture content for desorption is higher than for adsorption, at a particular water activity. The hysteresis effect extends over the entire water activity range for all samples but is most pronounced in
0.4
Ads
Des
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water Activity
Fig. 7. Sorption isotherms for potato starch powder at 45 C. Ads ¼ adsorption; Des ¼ desorption.
0.4 Ads
Des
-1
Moisture Content (kgkg DS)
agreement with Van den Berg (1981) and McMinn (1996) who observed Type II isotherm behaviour in potato and wheat starches, and potato starch gel, respectively. Starches consist of both crystalline and amorphous regions. The starch sorption isotherm is attributable to hydrogen-bonding of water molecules to the available hydroxyl groups of the substrate, i.e. those in the amorphous regions and on the surfaces of the crystallites (Urquhart, 1959). The crystalline regions typically exhibit resistance to solvent penetration. Hence, water affects the structure acting as a plasticizer of the amorphous regions. At low water activity the plasticizing affect is very small and the mobility of the amorphous regions is restricted. However, as the water activity increases, the sorbed moisture causes a subsequent swelling of the biopolymer, the degree of crystallinity decreases, and there is an increasing availability of the polar groups to the water molecules. Finally, the swelled polysaccharide forms a solution. In the low water activity range (aw < 0:25), potato starch, Amica and Hylon 7 have approximately equal water sorption capacities. This indicates that the starches have comparable sorption surfaces. Deviations in their sorption capacity in the higher water activity range may, for the most part, be due to differences with respect to the starch amorphous structure (Van den Berg, 1981). Van den Berg (1981) suggested that the deviation in the sorption capacity of starches is related to the glass transition range (0:3 > aw > 0:85) where the amorphous parts of starch start to plasticize. Urquhart (1959), however, attributed this deviation to the differences in the number of hydroxyl groups available. Van den Berg, Kaper, Weldring, and Wolters (1975) stated that potato starch has the highest water binding capacity of any starch, because it has the lowest degree of association between the starch molecules. The data also indicate that the equilibrium moisture content decreases with increasing temperature, at a constant water activity, thus indicating that starch becomes less hygroscopic. This trend may be due to a reduction in the total number of active sites for water binding as a result of physical and/or chemical changes in the product induced by temperature (Mazza & LeMaguer, 1980). Palipane and Driscoll (1992) suggested that at increased temperatures water molecules get activated to higher energy levels, causing them to become less stable and break away from the waterbinding sites of the food material, thus decreasing the equilibrium moisture content. As temperature varies, the excitation of molecules, as well as the distance, and thus attraction between molecules, varies. This causes the amount of sorbed water to change with temperature at a given relative humidity (Mohsenin, 1986). The equilibrium moisture content of potato starch powder exhibits a stronger temperature dependence
301
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water Activity
Fig. 8. Sorption isotherms for highly amylopectin powder at 45 C.
Moisture Content (kgkg -1 DS)
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Des
Table 3 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental adsorption data for potato starch powder
Ads
0.3
Model
Constants
30 C
45 C
60 C
GAB
X0 C K E (%)
0.035 17.6 0.907 10.3
0.027 11.8 0.905 10.8
0.021 8.19 0.889 15.0
Peleg
K1 K2 n1 n2 E (%)
0.255 0.106 9.92 0.682 5.68
0.117 0.178 1.12 18.3 11.1
0.117 0.062 9.11 0.866 12.1
FerroFontan
c a r E (%)
0.022 1.08 1.26 15.9
0.014 1.07 1.29 19.3
0.020 1.13 1.06 24.3
Henderson
A B E (%)
13.8 1.07 22.6
18.6 1.07 15.4
31.0 1.12 8.11
Oswin
A B E (%)
0.069 0.390 18.8
0.052 0.390 27.2
0.037 0.380 44.4
Halsey
A B E (%)
0.473 2.23 36.3
0.266 2.23 48.8
0.096 2.33 68.7
Mod-BET
A B E (%)
0.031 0.921 30.6
0.023 0.922 38.7
0.017 0.913 53.6
Smith
A B E (%)
0.008 )0.176 9.17
0.007 )0.132 4.51
0.006 )0.090 3.49
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Fig. 9. Sorption isotherms for highly amylose powder at 45 C.
the 0:3 < aw < 0:9 region. The magnitude of the hystersis loop is smaller for highly amylopectin and highly amylose than for potato starch. Highly amylopectin and highly amylose structures are more strongly associated internally than that of potato starch. This may account for the difference in water sorption capacity, as well as the extent of the hysteresis (Van den Berg, 1981). Highly amylose starch (30% amylopectin) shows a smaller hysteresis loop than the highly amylopectin starch (99.2% amylopectin) in the range aw > 0:7. This may be due to the different structure of the starches. Both amylose and amylopectin are fully amorphous, however, due to the much easier coagulation of amylose during the separation process of amylose and amylopectin, amylose will be more strongly internally associated than amylopectin, with its branched structure (Van den Berg, 1981). The trend of the hysteresis phenomena is similar to those reported for potato by Wang and Brennan (1991), and McMinn and Magee (1999). Hysteresis is not fully understood, although there is general agreement that some thermodynamically irreversible processes must occur during desorption or adsorption, or both. The most favoured theory used to explain this thermodynamical oddity suggests that in the wet condition polar sites in the molecular structure of the material are almost entirely satisfied by adsorbed water. Upon drying and shrinkage, the molecules and their water-holding sites are drawn closely enough together to satisfy each other. This reduces the waterholding capacity of the material upon subsequent adsorption (Mohsenin, 1986). 3.3. Mathematical modelling The parameters for the sorption models for potato, highly amylopectin and highly amylose starch powders are shown in Tables 3–8, together with the mean relative percentage deviation moduli ðEÞ. Examination of the results in Tables 3 and 4 indicates that the Peleg model best describes the experimental adsorption and desorption data for potato starch
throughout the entire range of water activity. The Peleg model gives E values ranging from 5.68% to 12.4%, with average values of 9.63% for adsorption and 9.59% for desorption; this compares with average E values for the GAB model of 12.0% for adsorption and 10.1% for desorption. Peleg (1993), Rahman, Perera, and Thebaud (1998) and Delgado and Da-Wen Sun (2002) reported that the Peleg model provided a good description of the isotherms of potato starch, peas and cured beef, respectively. Van den Berg (1984), McMinn and Magee (1999) and Timmermann, Chirife, and Iglesias (2001) reported that the GAB model adequately represented the sorption isotherms of potato, wheat starch, potato and starchy materials. In the range of water activity 0:35 < aw < 0:9, the Smith model is shown to give the closest fit to the experimental data, giving an average E value of 5.72% for adsorption. Young (1976) applied the Smith model to adsorption and desorption isotherms of peanuts, and concluded that the model could be used for describing the isotherms provided that the water activity was above 0.30.
A.H. Al-Muhtaseb et al. / Journal of Food Engineering 61 (2004) 297–307 Table 4 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental desorption data for potato starch powder 60 C
303
Table 5 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental adsorption data for highly amylose powder
Model
Constants
30 C
45 C
Model
Constants
30 C
45 C
GAB
X0 C K E (%)
0.056 12.1 0.88 12.2
0.046 8.24 0.888 10.9
0.029 6.38 0.917 7.18
GAB
X0 C K E (%)
0.031 11.1 0.913 5.54
0.028 8.52 0.893 17.8
0.028 6.04 0.91 7.18
Peleg
K1 K2 n1 n2 E (%)
0.343 0.096 3.86 0.473 9.24
0.110 0.283 0.664 7.53 12.4
0.235 0.100 10.9 1.00 7.14
Peleg
K1 K2 n1 n2 E (%)
0.102 0.236 0.861 10.6 6.05
0.083 0.198 0.926 7.05 4.54
0.209 0.068 7.86 0.737 5.09
FerroFontan
c a r E (%)
0.270 1.57 0.620 13.4
0.056 1.15 0.999 16.7
0.029 1.09 1.05 15.1
FerroFontan
c a r E (%)
0.021 1.07 1.21 11.1
0.079 1.23 0.77 10.4
0.036 1.13 0.965 6.78
Henderson
A B E (%)
12.6 1.35 17.4
12.8 1.12 18.3
12.9 0.940 17.3
Henderson
A B E (%)
13.5 0.995 20.2
16.7 1.06 10.6
15.9 0.993 17.5
Oswin
A B E (%)
0.121 0.324 39.9
0.083 0.374 32.0
0.055 0.424 32.7
Oswin
A B E (%)
0.059 0.410 20.8
0.056 0.392 52.1
0.051 0.407 28.2
Halsey
A B E (%)
0.663 2.64 52.8
0.583 2.33 49.8
0.490 2.09 55.3
Halsey
A B E (%)
0.423 2.19 44.6
0.315 2.23 79.5
0.322 2.17 45.2
Mod-BET
A B E (%)
0.059 0.879 43.7
0.038 0.912 43.8
0.025 0.933 45.3
Mod-BET
A B E (%)
0.027 0.925 35.6
0.026 0.918 68.6
0.023 0.926 33.1
Smith
A B E (%)
0.047 )0.225 17.4
0.016 )0.197 12.1
)0.006 )0.168 8.64
Smith
A B E (%)
0.0002 )0.168 6.49
0.003 )0.149 6.34
)0.004 )0.146 5.41
The Halsey model least adequately represented the experimental data, giving an average E value of 51.3% for adsorption and 52.6% for desorption. Wang and Brennan (1991) reported that the Halsey model was inadequate for representing the sorption isotherms of potato, giving an average E value of 70.4%. The Henderson, Oswin and Mod-BET model failed to describe the experimental data giving an average E value above 20%. Wang and Brennan (1991) and Menkov (2000) reported that the Henderson model failed to describe the sorption isotherms of potato and lentil seeds, respectively. Examination of the results for the highly amylose starch powder (Tables 5 and 6) revealed similar observations. The Peleg model gave the best description of the experimental data with E values ranging from 4.54% to 6.20%, and an average value of 5.23% for adsorption and 6.05% for desorption. The GAB model provided a good description of the data with an average E value of 6.17% for adsorption and 4.64% for desorption. The Ferro-Fontan model gave a similar result with an average E value of 9.43% for adsorption and 5.96% for
60 C
desorption. The Smith model also adequately fitted the results with an average E value of 6.08% for adsorption and 4.10% for desorption, in the range 0:35 < aw < 0:9. Once again, the Halsey model was inadequate, giving the highest average E values of 56.4% for adsorption and 44.2% for desorption. As shown in Tables 5 and 6, other models were fitted to the experimental data. On examining the E values of the Henderson, Oswin and Mod-BET models, these were found to be unsuitable for representation of the results. In the case of highly amylopectin starch powder (Tables 7 and 8), the Ferro-Fontan model provided the best representation of the experimental data throughout the entire range of water activity, with an average E value of 7.41% for adsorption and 3.59% for desorption. Iglesias and Chirife (1995) reported that the FerroFontan equation accurately represented the sorption isotherm of 92 different food products (starches, proteins, cereals, meats, vegetables, etc.) in the range of water activity 0.1–0.9, with only 2–4% average error in the predicted moisture content. The GAB model was the
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Table 6 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental desorption data for highly amylose powder 45 C
60 C
Table 7 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental adsorption data for highly amylopectin powder
Model
Constants
30 C
Model
Constants
30 C
45 C
GAB
X0 C K E (%)
0.043 10.2 0.89 7.14
0.037 7.50 0.881 4.81
0.036 5.13 0.880 1.98
GAB
X0 C K E (%)
0.032 22.2 0.888 6.19
0.032 15.3 0.882 9.24
0.027 9.86 0.887 6.21
Peleg
K1 K2 n1 n2 E (%)
0.270 0.094 6.81 0.582 6.08
0.094 0.202 0.754 7.45 5.87
0.179 0.101 8.42 0.96 6.20
Peleg
K1 K2 n1 n2 E (%)
0.193 0.080 7.51 0.557 7.40
0.097 0.166 0.777 8.96 12.9
0.139 0.099 12.1 1.02 10.5
FerroFontan
c a r E (%)
0.046 1.14 1.06 3.53
0.045 1.16 1.00 4.37
0.050 1.18 0.932 9.98
FerroFontan
c a r E (%)
0.022 1.11 1.23 4.52
0.024 1.12 1.19 6.8
0.020 1.11 1.16 10.9
Henderson
A B E (%)
13.7 1.12 17.3
17.9 1.15 13.6
18.5 1.12 8.94
Henderson
A B E (%)
21.2 1.19 17.2
22.9 1.20 13.2
24.5 1.15 12.8
Oswin
A B E (%)
0.078 0.374 20.1
0.065 0.368 25.9
0.059 0.374 38.1
Oswin
A B E (%)
0.062 0.357 14.2
0.059 0.355 17.8
0.050 0.367 26.2
Halsey
A B E (%)
0.489 2.33 34.7
0.294 2.36 40.7
0.278 2.34 57.3
Halsey
A B E (%)
0.216 2.42 26.4
0.197 2.44 28.3
0.163 2.38 40.4
Mod-BET
A B E(%)
0.036 0.911 24.9
0.030 0.908 30.1
0.027 0.911 45.1
Mod-BET
A B E (%)
0.028 0.904 17.4
0.027 0.902 17.8
0.023 0.909 29.8
Smith
A B E (%)
0.011 )0.189 4.03
0.012 )0.151 4.06
0.010 )0.143 4.21
Smith
A B E (%)
0.016 )0.135 3.89
0.017 )0.128 2.95
0.012 )0.114 4.43
next best with an average E value of 7.24% for adsorption and 6.17% for desorption, followed by the Peleg model with an average E value of 10.27% for adsorption and 6.72% for desorption. A similar observation was found for the Smith model with an average E value of 3.76% for adsorption and 5.18% for desorption in the range 0:35 < aw < 0:9. Once again, the Halsey, Henderson, Oswin and Mod-BET models failed to adequately represent the sorption isotherms. On comparison of all the data, it can be concluded, that the Peleg, GAB and Ferro-Fontan models provide a good description of moisture sorption isotherms for all materials, at all temperatures, throughout the entire range of water activity, with the Smith model being satisfactory in the range 0:35 < aw < 0:9. The Halsey, Henderson, Oswin and Mod-BET models failed to adequately describe the experimental data for all materials in the temperature range. It should be noted that, although the Peleg and Smith models provide a good representation of the data, this is only mathematical and provides no indication of the nature of the sorption process.
60 C
3.4. Guggenheim–Anderson–de Boer model Further examination of the GAB parameters (Tables 3–8) shows that, for adsorption, the values of the monolayer moisture content, X0 are lower, and those of the Guggenheim constant C are higher than for desorption. In terms of the sorption phenomenon this means that during adsorption although less sorption sites are available, they have a greater binding energy, with the multi-layer molecules deviating more from the free bulk water (Van den Berg, 1984). Furthermore, the X0 values for all three materials show a tendency to decrease with an increase in temperature. This decrease in mono-layer moisture content can be explained by considering the structural changes in starch polymers at increased temperature. The degree of hydrogen bonding in such polymers is reduced with increasing temperature, thereby decreasing the availability of active sites for water binding and thus, the mono-layer moisture content (Westgate, Lee, & Ladisch, 1992). The Guggenheim constant was also shown to decrease with increasing temperature, indicating the ex-
A.H. Al-Muhtaseb et al. / Journal of Food Engineering 61 (2004) 297–307 Table 8 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental desorption data for highly amylopectin powder Model
Constants
30 C
45 C
GAB
X0 C K E (%)
0.041 14.59 0.902 7.58
0.041 9.13 0.881 8.06
0.034 6.79 0.89 6.09
Peleg
K1 K2 n1 n2 E (%)
0.284 0.109 8.32 0.661 8.63
0.097 0.225 0.671 7.12 7.88
0.200 0.073 6.84 0.65 3.65
FerroFontan
c a r E (%)
0.034 1.10 1.15 2.82
0.045 1.15 1.04 3.41
0.045 1.16 0.962 4.53
Henderson
A B E (%)
12.3 1.07 18.9
16.6 1.167 14.5
18.9 1.12 15.2
Oswin
A B E (%)
0.078 0.386 16.0
0.072 0.363 20.9
0.059 0.371 24.4
Halsey
A B E (%)
0.591 2.26 30.7
0.354 2.40 35.1
0.255 2.36 38.1
Mod-BET
A B E (%)
0.035 0.918 21.8
0.033 0.905 24.3
0.027 0.911 25.78
Smith
A B E (%)
0.008 )0.20 4.64
0.016 )0.164 5.53
0.009 )0.14 5.38
Table 9 Characteristic GAB parameters (Eqs. (8) and (9)) for potato starch powder c0
DHc (kJ mol1 )
k0
DHk (kJ mol1 )
0.004 0.009
21.4 18.0
0.729 1.45
0.556 )1.27
60 C
pected tendency of a decrease in binding energy for the first adsorbed layer with increasing temperature. Such a decrease indicates an increasingly shorter residence time for the adsorbed water molecules in the first layer, with the character of the adsorption process becoming less strongly localized (Calzetta Resio, Aguerre, & Suarez, 1999). A clear correlation of the constant K with temperature was not observed. Van den Berg (1984) stated that the parameters C and K incorporate the temperature effect. C is more enthalpic while K is more entropic in nature. Therefore, when describing practical isotherms over limited temperature intervals, it may suffice to incorporate the temperature effect only in C. A more detailed analysis of the GAB parameters can provide further valuable information about adsorption and desorption. A direct non-linear regression technique was adopted, with Eqs. (8) and (9) being substituted into Eq. (7). The results of the regression analysis are summarized in Tables 9–11. DHc represents the difference in enthalpy between mono-layer and multi-layer sorption (Van den Berg, 1984). The large positive value calculated is as
305
Adsorption Desorption
Table 10 Characteristic GAB parameters (Eqs. (8) and (9)) for highly amylopectin powder
Adsorption Desorption
c0
DHc (kJ mol1 )
k0
DHk (kJ mol1 )
0.003 0.003
22.6 21.5
0.825 0.723
0.188 0.545
Table 11 Characteristic GAB parameters (Eqs. (8) and (9)) for highly amylopectin powder
Adsorption Desorption
c0
DHc (kJ mol1 )
k0
DHk (kJ mol1 )
0.014 0.005
16.9 19.1
0.716 0.783
0.617 0.320
expected and is due to the strong exothermic interaction of water vapour with the primary sorption sites of starch matrix. DHk represents the difference between the heat of condensation of water and the heat of sorption of the multi-layer, which is expected to have a positive value due to the exothermic nature of moisture sorption (Van den Berg, 1984). The relatively lower magnitudes of DHk observed implies the presence of less firmly bound multilayer molecules, at intermediary energy levels between those of mono-layer molecules and the bulk liquid. The small negative value of DHk , in the case of potato starch, indicates that the heat of sorption of the multi-layer is greater than the heat of condensation of water, due to the endothermic dissolution of small molecular solutes. The DHc value for adsorption is slightly higher than the value for desorption, in the case of potato and highly amylopectin starch, and lower in the case of highly amylose starch. The variation in enthalpy values between adsorption and desorption suggests a degree of irreversibility with respect to the water binding properties of the material (McMinn & Magee, 1999).
4. Conclusions On the basis of this work the following conclusions can be drawn: • Potato starch, highly amylopectin and highly amylose powders present Type II isotherms.
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• Temperature affects the sorption behaviour; the equilibrium moisture content decreases with increasing temperature, at constant water activity. • Hysteresis is evident over the entire range of water activity for all materials. • Within the temperature range investigated, the models developed by the empirical four parameter (Peleg), the kinetic three parameter (GAB) and the semi empirical three parameter Ferro-Fontan were found to best represent the experimental data in the water activity range 0.05–0.95; the Smith model gave the best fit in the range 0.3–0.95.
References Aguerre, R. J., Suarez, C., & Viollaz, P. E. (1989). New BET type multiplayer sorption isotherms. Part II: Modelling water sorption in foods. Lebensmittel-Wissenchaft und Technology, 22, 192–195. Aguilera, J. M., & Stanley, D. W. (1999). Microstructural principles of food processing and engineering (pp. 373–411). Maryland: Aspen Publication. AOAC (1980). Official methods of analysis. Washinghton, DC: Association of Official Analytical Chemists Inc. Bizot, H. (1983). Using the GAB model to construct sorption isotherms. In Jowitt et al. (Eds.), Physical properties of foods (pp. 43–54). New York: Applied Science. Brunauer, S., Deming, L. S., Deming, W. E., & Troller, E. (1940). On the theory of Van der Waals adsorption of gases. Journal of the American Chemical Society, 62, 1723–1732. Calzetta Resio, A., Aguerre, R. J., & Suarez, C. (1999). Analysis of the sorptional characteristics of amaranth starch. Journal of Food Engineering, 42, 51–57. Chirife, J., & Iglesias, H. A. (1978). Equations for fitting water sorption isotherms of foods: part 1. A review. Journal of Food Technology, 13, 159–174. Chirife, J., Bouquet, R., Ferro-Fontan, C., & Iglesias, H. A. (1983). A new model for describing the water sorption isotherm of foods. Journal of Food Science, 48, 1382–1383. Delgado, A. E., & Da-Wen Sun (2002). Desorption isotherms for cooked and cured beef and pork. Journal of Food Engineering, 51, 163–170. Ferro-Fontan, C., Chirife, J., Sancho, E., & Iglesias, H. A. (1982). Analysis of a model for water sorption phenomena in foods. Journal of Food Science, 47, 1590–1594. Halsey, G. (1948). Physical adsorption on non-uniform surfaces. Journal of Chemistry Physics, 16, 931–937. Henderson, S. M. (1952). A basic concept of equilibrium moisture. Agricultural Engineering, 33, 29–32. Iglesias, H. A., Chirife, J., & Lombardi, J. L. (1975). Comparison of water vapour sorption by sugar beet root components. Journal of Food Technology, 10, 385–391. Iglesias, H. A., & Chirife, J. (1976). A model for describing the water sorption behaviour of foods. Journal of Food Science, 41, 984–992. Iglesias, H. A., & Chirife, J. (1995). An alternative to the Guggenheim, Anderson and de Boer model for the mathematical description of moisture sorption isotherms of foods. Food Research International, 28, 317–321. Kapsalis, J. G. (1981). Moisture sorption hysteresis. In L. B. Rockland, & G. F. Stewart (Eds.), Water Activity: Influences on Food Quality (pp. 143–177). New York: Academic Press. Labuza, T. P. (1975). Interpretation of sorption data in relation to the state of constituent water. In R. Duckworth (Ed.), Water relations in foods (pp. 155–172). New York: Academic Press.
Labuza, T. P. (1980). The effect of water activity on reaction kinetics of food deterioration. Food Technology (April), 36–59. Leung, H. K. (1983). Water activity and other colligative properties of foods. In ASAE annual meeting, Chicago, paper no. 83,6508. Lomauro, C. J., Bakshi, A. S., & Labuza, T. P. (1985). Evaluation of food moisture sorption isotherm equations. Part I. Fruit, vegetable and meat products. Lebensmittel-Wissenchaft und Technology, 18, 111–117. Mazza, G., & LeMaguer, M. (1980). Dehydration of onion: some theoretical and practical considerations. Journal of Food Technology, 15, 181–194. McMinn, W. A. M. (1996). Transport and thermophysical property variations during the convective drying of starch materials. Ph.D. Thesis, School of Chemical Engineering, QueenÕs University Belfast, UK. McMinn, W. A. M., & Magee, T. R. A. (1999). Studies on the effect of temperature on the moisture sorption characteristics of potatoes. Journal of Food Process Engineering, 22, 113–128. Menkov, N. D. (2000). Moisture sorption isotherms of lentil seeds at several temperatures. Journal of Food Engineering, 44, 205–211. Mohsenin, N. (1986). Physical properties of plant and animal materials. New York: Gordon & Breach. Oswin, C. R. (1946). The kinetics of package life III. The isotherm. Journal of Chemical Industry, 65, 419–421. Palipane, K. B., & Driscoll, R. H. (1992). Moisture sorption characteristics of inshell macadamia nuts. Journal of Food Engineering, 18, 63–76. Peleg, M. (1993). Assessment of a semi-empirical four parameter general model for sigmoid moisture sorption isotherms. Journal of Food Process Engineering, 16, 21–37. Rahman, M. S., Perera, C. O., & Thebaud, C. (1998). Desorption isotherm and heat pump drying kinetics of peas. Food Research International, 30, 485–491. Rizvi, S. S. H. (1995). Thermodynamic properties of food in dehydration. In M. A. Rao, & S. S. H. Rizvi (Eds.), Engineering properties of foods (pp. 223–309). New York: Marcel-Dekker. Ruegg, M. (1980). Calculation of the activity of water in sulphuric acid solutions at various temperature. Lebensmittel-Wissenchaft und Technology, 13, 22–24. Scott, N. F. (1957). Water relations of food spoilage microorganism. In Advances in Food Research (Vol. III). New York: Academic Press. Smith, S. E. (1947). The sorption of water vapour by high polymers. Journal of the American Chemical Society, 69, 646. Timmermann, E. O. (1989). A BET-like three sorption stage isotherm. Journal of Chemical Society, Faraday Transaction, 85, 1631– 1645. Timmermann, E. O., Chirife, J., & Iglesias, H. A. (2001). Water sorption isotherms of foods and foodstuffs: BET or GAB parameters? Journal of Food Engineering, 48, 19–31. Urquhart, A. R. (1959). Sorption of water by cellulose and starch. In J. Honeyman (Ed.), Recent advances in the chemistry of cellulose and starch (pp. 240–264). London: Heywood & Company. Van den Berg, C., Kaper, F. S., Weldring, J. A. G., & Wolters, I. (1975). Water binding by potato starch. Journal of Food Technology, 10, 589–602. Van den Berg, C. (1981). Vapour sorption equilibria and other water– starch interactions: a physico-chemical approach. Ph.D. Thesis, Agricultural University Wageningen. The Netherlands. Van den Berg, C., & Bruin, S. (1981). Water activity and its estimation in food systems. In L. B. Rockland, & G. F. Stewart (Eds.), Water activity: influences on food quality (pp. 147–177). New York: Academic Press. Van den Berg, C. (1984). Description of water activity of foods for engineering purposes by means of the GAB model of sorption. In B. M. McKenna (Ed.), Engineering and food (Vol. 1, pp. 311–321). New York: Elsevier Applied Science.
A.H. Al-Muhtaseb et al. / Journal of Food Engineering 61 (2004) 297–307 Wang, N., & Brennan, J. G. (1991). Moisture sorption isotherm characteristics of potatoes at four temperatures. Journal of Food Engineering, 14, 269–282. Westgate, P., Lee, J. Y., & Ladisch, M. R. (1992). Modelling of equilibrium sorption of water vapour on starchy materials. American Society of Agricultural Engineers, 35, 213–219.
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Wolf, W., Spiess, W. E. L., & Jung, G. (1985). Standarization of isotherm measurements. In D. Simatos, & J. L. Multon (Eds.), Properties of water in foods (pp. 661–679). The Netherlands: Martinus Nijhoff. Young, J. H. (1976). Evaluation of models to describe sorption and desorption equilibrium moisture content isotherms of Virginia-type peanuts. Transaction ASAE, 19, 146.
Water sorption isotherms of starch powders Part 1: mathematical description of experimental data A.H. Al-Muhtaseb, W.A.M. McMinn, T.R.A. Magee
*
Food Process Engineering Research Group, School of Chemical Engineering, QueenÕs University Belfast, David Keir Building Stranmillis Road, Belfast, BT9 5AG, UK Received 20 January 2003; accepted 13 April 2003
Abstract Adsorption and desorption isotherms for potato, highly amylopectin and highly amylose starch powders were determined at 30, 45 and 60 C using a gravimetric technique. Samples were equilibrated in desiccators containing sulphuric acid solutions of known water activity (0.05–0.95), and placed in temperature-controlled cabinets for approximately three weeks. The starch powders exhibited Type II behaviour. The sorption capacity decreased with increasing temperature. The data obtained were fitted to several models including two parameter relationships (Halsey, Oswin, Henderson, Modified-BET and Smith), three parameter equations (GAB, Ferro-Fontan) and four parameter equation (Peleg). A non-linear least square regression program was used to evaluate the models constants. The empirical Peleg model followed by the kinetic GAB and the semi empirical Ferro-Fontan models were found to best represent the experimental data in the water activity range 0.05–0.95. In the range of water activity 0.35–0.95 the Smith model was shown to give the closest fit to the experimental data. 2003 Elsevier Ltd. All rights reserved. Keywords: Sorption isotherm; Potato starch; Highly amylopectin starch; Highly amylose starch; Mathematical models; Hysteresis
1. Introduction Control of moisture content during the processing of foods is an ancient method of preservation, and probably humankindÕs first ‘‘technology’’ for extending the stability of foods. This is achieved by either removing, or binding water such that the food becomes stable to both microbial and chemical deterioration (Labuza, 1980). The most common limitation on the shelf life of food is microbial growth, hence several preservation processes are aimed at achieving stability of foods by reducing the moisture content to levels below those required by micro-organisms for survival and reproduction (Aguilera & Stanley, 1999). Sorption characteristics have, and are currently being examined in light of their influence on the storage stability of dehydrated products, as well as their affect on the diffusion of water vapour.
*
Corresponding author. Tel.: +44-(0)28-9027-4255; fax: +44-(0)289038-1753. E-mail address: [email protected] (T.R.A. Magee). 0260-8774/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0260-8774(03)00133-X
In 1957, Scott termed the equilibrium relative humidity, i.e. availability of water in food, water activity (Scott, 1957). The work was widely acclaimed and led to a rapid expansion in the use of water activity, denoted (aw ), which is now one of the major control variables in food preservation technology (Van den Berg & Bruin, 1981). Water activity is a term indicating the ‘‘quality’’ of the water content of food. It describes the degree of ‘‘boundness’’ of water and, hence its availability to participate in physical, chemical, and microbiological reactions. The relationship between the total moisture content and water activity of the food, over a range of values, at a constant temperature and under equilibrium conditions, yields a moisture sorption isotherm when expressed graphically. This isotherm curve can be obtained in one of two ways; adsorption or desorption. The adsorption and desorption processes are not fully reversible, therefore a distinction can be made between the isotherms by determining whether the moisture levels within the product are increasing or decreasing. The effect of temperature on the sorption isotherm is of great importance given that foods are exposed to a
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Nomenclature A aw B C c0 E DHc DHk
K k0
constant (dimensionless) water activity constant (dimensionless) GAB model parameter (dimensionless) constant (adjusted to the temperature effect) (dimensionless) mean relative percentage deviation modulus (%) difference in enthalpy between mono-layer and multi-layer sorption (J mol1 ) difference between the heat of condensation of water and the heat of sorption of the multilayer (J mol1 ) GAB model parameter (dimensionless) constant (adjusted to the temperature effect) (dimensionless)
range of temperatures during storage and processing, and water activity changes with temperature. Temperature affects the mobility of the water molecules, and the dynamic equilibrium between the vapour and adsorbed phases. In the field of water vapour sorption by a solid sorbent, moisture sorption hysteresis is the phenomena by which two different paths exist between the adsorption and desorption isotherms (Kapsalis, 1981). The effect of hysteresis on food is important, even though it can be relatively low in magnitude. Rizvi (1995) stated that the extent of hysteresis is related to the nature and state of the components in a food. It may reflect their structural and conformational rearrangement, which alters the accessibility of energetically favourable polar sites and thus, may hinder the movement of moisture. Iglesias and Chirife (1976) recognized that it is not possible to give a single explanation of the hysteresis phenomena in foods, due to food being a complex combination of various constituents, which can, not only sorb water independently but also, interact among themselves. Water sorption isotherm equations are useful for predicting water sorption properties of foods, although they provide little insight into the interaction of water and food components (Leung, 1983). Although several mathematical models exist to describe water sorption isotherms of food materials (Iglesias, Chirife, & Lombardi, 1975), no one equation gives accurate results throughout the whole range of water activities, or for all types of foods. Labuza (1975) attributed this to the fact that the water is associated with the food matrix by different mechanisms in different water activity regions. Models available in the literature to describe moisture sorption isotherm can be divided into several categories;
K1 , K2 mi mpi N n 1 , n2 R r T X X0 a c h
equation parameters (dimensionless) experimental value predicted value number of experimental data equation parameters (dimensionless) universal gas constant (8.314 J mol1 K1 ) equation parameter (dimensionless) temperature (K) equilibrium moisture content (kg kg1 dry solid) mono-layer moisture content (kg kg1 dry solid) equation parameter (dimensionless) equation parameter (dimensionless) equation parameter (dimensionless)
kinetic models based on a mono-layer (Mod-BET model), kinetic models based on a multi-layer and condensed film (GAB model), semi-empirical (FerroFontan, Henderson and Halsey models) and empirical models (Smith and Oswin models). The BET model represents a fundamental milestone in the interpretation of multi-layer sorption isotherms, particularly Types II and III (Timmermann, 1989). Many researchers modified the BET model and the modified equation gave a good fit up to water activity 0.9 (Aguerre, Suarez, & Viollaz, 1989). The GAB model is considered to be the most versatile sorption model available in the literature and has been adopted by a group of West European food researchers COST 90 (Bizot, 1983; Van den Berg & Bruin, 1981). Chirife, Bouquet, Ferro-Fontan, and Iglesias (1983) proposed the Ferro-Fontan model. Iglesias and Chirife (1995) reported that the Ferro-Fontan equation accurately represented the sorption isotherm of 92 different food products. Peleg (1993) proposed a fourparameter model and noted that the model can be used for both sigmoidal and non-sigmoidal isotherms, and that it fitted as well as, or better than, the GAB model. The Smith model (1947) is useful in describing the sorption isotherm of biological materials such as starch and cellulose. Henderson (1952) proposed a semi-empirical model for the equilibrium moisture content of cereal grains. Chirife and Iglesias (1978) found that Halsey and Oswin models are also versatile. The objectives of this study were to provide reliable experimental data for the sorption characteristics of starch powders (potato, highly amylopectin, highly amylose) to model the sorption isotherms using selected equations, determine their dependence on temperature, and examine the hysteresis phenomena.
A.H. Al-Muhtaseb et al. / Journal of Food Engineering 61 (2004) 297–307
2. Materials and methods 2.1. Experimental procedure The equilibrium moisture contents of potato (80% amylopectin, 20% amylose) (Roquette, UK), highly amylopectin (99.2% amylopectin, 0.8% amylose) and highly amylose (30% amylopectin, 70% amylose) (National Starch and Chemicals, UK) starch powders were determined by a gravimetric technique, in which the weight was monitored discontinuously within a standard static system of thermally stabilized desiccators. This method was recommended by the COST 90 project (Wolf, Spiess, & Jung, 1985). For adsorption a 6 ± 0.001 g sample of the bone dry powder was placed in a petri-dish inside a dessicator. For desorption, a 12 ± 0.001 g sample of 1 kg kg1 dry basis powder was used. Each experiment was carried out in triplicate. Sulphuric acid (Fisher Scientific, UK) solutions were used to maintain the specified relative humidity inside the desiccators. The effect of temperature and acid concentration on the equilibrium relative humidity val-
Table 1 Water activity of sulphuric acid solutions at selected concentrations and temperatures H2 SO4 solution % (v/v) 5 20 30 40 50 60 70 80
Water activity (aw ) 30 C
45 C
60 C
0.9808 0.8814 0.7549 0.5711 0.3574 0.1677 0.047 0.0059
0.9812 0.8839 0.7629 0.5866 0.3765 0.1834 0.0548 0.0077
0.9818 0.8882 0.7711 0.5989 0.3936 0.1988 0.0611 0.0103
299
ues of sulphuric acid solutions are presented in Table 1 (Ruegg, 1980). The prepared dessicators were then placed in temperature-controlled cabinets maintained at 30, 45 and 60 ± 1 C. The samples were allowed to equilibrate until there was no discernible weight change, as evidenced by constant weight values (±0.001 g). This involved a period of approximately three weeks for potato starch powder and two weeks for highly amylopectin and highly amylose powders. The total time required for removal, weighing and replacing the samples in the desiccators was approximately 30 s. This minimized the degree of atmospheric moisture sorption during weighing. Each experiment was carried out in triplicate. The bone dry mass was determined gravimetrically by drying in a convectional oven at 105 C for 8–10 h (AOAC, 1980).
2.2. Data analysis The isotherm models used to fit the data are presented in Table 2. A non-linear least square regression analysis was used to evaluate the model parameters. To evaluate the goodness of fit of each model, the mean relative percentage deviation modulus ðEÞ was used, which is defined by
E¼
N 100 X jmi mpi j N i¼1 mi
ð11Þ
where mi is the experimental value, mpi is the predicted value, and N is the number of experimental data. The mean relative percentage deviation modulus ðEÞ is widely adopted throughout the literature, with a modulus value below 10% indicative of a good fit for practical purposes (Lomauro, Bakshi, & Labuza, 1985).
Table 2 Isotherm equations for experimental data fitting Model
Mathematical expression
Mod-BET (Aguerre et al., 1989)
X ¼ X0 Caw =½ð1 aw Þð1 C lnð1 aw ÞÞ
ð1Þ
Halsey (Halsey, 1948)
X ¼ ½A=ðT ln aw Þ1=B
ð2Þ
Smith (Smith, 1947)
X ¼ A þ ðB logð1 aw ÞÞ
ð3Þ
Henderson (Henderson, 1952)
X ¼ ½ lnð1 aw Þ=A
Oswin (Oswin, 1946)
X ¼ Aðaw =ð1 aw ÞÞB
Ferro-Fontan (Ferro-Fontan, Chirife, Sancho, & Iglesias, 1982) Guggenheim–Anderson–de Boer (Van den Berg & Bruin, 1981)
Peleg (Peleg, 1993)
1=B
1=r
X ¼ ½c= lnða=aw Þ
ð4Þ ð5Þ ð6Þ
X ¼ X0 CKaw =½ð1 Kaw Þð1 Kaw þ CKaw Þ
ð7Þ
C ¼ c0 expðDHC =RT Þ
ð8Þ
K ¼ k0 expðDHK =RT Þ
ð9Þ
X ¼
K1 anw1
þ
K2 anw2
ð10Þ
300
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3. Results and discussion 3.1. Desorption and adsorption isotherms The adsorption and desorption isotherms for potato, highly amylopectin and highly amylose starch powders at 30, 45 and 60 C are shown in Figs. 1–6. The equilibrium moisture content at each water activity repre-
Moisture Content (kgkg -1 DS)
Moisture Content (kgkg -1 DS)
0.4
0.3
0.2
0.1
0.0 0.2
0.4 0.6 Water Activity 60°C
45°C
0.8
1.0
0.3
0.2
0.1
0.0
0.2
30°C
0.4 0.6 Water Activity 60°C
Fig. 1. Experimental adsorption isotherms for potato starch powder. DS ¼ dry basis.
45°C
0.8
1.0
30°C
Fig. 4. Experimental desorption isotherms for highly amylopectin powder.
0.4
0.4
-1
Moisture Content (kgkg DS)
Moisture Content (kgkg -1 DS)
0.4
0.0
0.0
0.3
0.2
0.1
0.0
0.3
0.2
0.1
0.0
0.0
0.2
0.4 0.6 Water Activity 60°C
45°C
0.8
1.0
0.0
0.2
30°C 30°C
0.4 0.6 Water Activtiy 60°C
Fig. 2. Experimental desorption isotherms for potato starch powder.
45°C
0.8
1.0
30°C
Fig. 5. Experimental adsorption isotherms for highly amylose powder.
0.4
0.4
Moisture Content (kgkg DS)
0.3
-1
Moisture Content (kgkg -1 DS)
sents the mean value of three replications. Without exception, the adsorption and desorption isotherms demonstrate an increase in equilibrium moisture content with increasing water activity, at a constant temperature. This behaviour is manifested in the form of a sigmoidal shaped curve, thus reflecting a Type II isotherm (according to BrunauerÕs classification) (Brunauer, Deming, Deming, & Troller, 1940). This is in
0.2 0.1 0.0 0.0
0.2
0.4 0.6 Water Activity 60°C
45°C
0.8
1.0
0.3
0.2
0.1
0.0 0.0
0.2
0.4 0.6 Water Activity
30°C 60°C
Fig. 3. Experimental adsorption isotherms for highly amylopectin powder.
45°C
0.8
1.0
30°C
Fig. 6. Experimental desorption isotherms for highly amylose powder.
A.H. Al-Muhtaseb et al. / Journal of Food Engineering 61 (2004) 297–307
than the highly amylopectin and highly amylose powders, particularly in the high water activity range aw > 0:85. In general, the effect of temperature on desorption is more noticeable; an exception to this behaviour was found in the case of potato starch powder at aw > 0:90. The temperature shifts observed have an important practical affect on the chemical and microbiological reactions which cause quality deterioration. An increase in temperature causes an increase in the water activity, at the same moisture content, which in turn causes an increase in the reaction rates leading to quality deterioration (Van den Berg & Bruin, 1981).
3.2. Moisture sorption hysteresis
Moisture Content (kgkg -1 DS)
Figs. 7–9 show the sorption isotherms obtained at 45 C for potato, highly amylopectin and highly amylose starch powders, respectively. The graphs clearly show that the equilibrium moisture content for desorption is higher than for adsorption, at a particular water activity. The hysteresis effect extends over the entire water activity range for all samples but is most pronounced in
0.4
Ads
Des
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water Activity
Fig. 7. Sorption isotherms for potato starch powder at 45 C. Ads ¼ adsorption; Des ¼ desorption.
0.4 Ads
Des
-1
Moisture Content (kgkg DS)
agreement with Van den Berg (1981) and McMinn (1996) who observed Type II isotherm behaviour in potato and wheat starches, and potato starch gel, respectively. Starches consist of both crystalline and amorphous regions. The starch sorption isotherm is attributable to hydrogen-bonding of water molecules to the available hydroxyl groups of the substrate, i.e. those in the amorphous regions and on the surfaces of the crystallites (Urquhart, 1959). The crystalline regions typically exhibit resistance to solvent penetration. Hence, water affects the structure acting as a plasticizer of the amorphous regions. At low water activity the plasticizing affect is very small and the mobility of the amorphous regions is restricted. However, as the water activity increases, the sorbed moisture causes a subsequent swelling of the biopolymer, the degree of crystallinity decreases, and there is an increasing availability of the polar groups to the water molecules. Finally, the swelled polysaccharide forms a solution. In the low water activity range (aw < 0:25), potato starch, Amica and Hylon 7 have approximately equal water sorption capacities. This indicates that the starches have comparable sorption surfaces. Deviations in their sorption capacity in the higher water activity range may, for the most part, be due to differences with respect to the starch amorphous structure (Van den Berg, 1981). Van den Berg (1981) suggested that the deviation in the sorption capacity of starches is related to the glass transition range (0:3 > aw > 0:85) where the amorphous parts of starch start to plasticize. Urquhart (1959), however, attributed this deviation to the differences in the number of hydroxyl groups available. Van den Berg, Kaper, Weldring, and Wolters (1975) stated that potato starch has the highest water binding capacity of any starch, because it has the lowest degree of association between the starch molecules. The data also indicate that the equilibrium moisture content decreases with increasing temperature, at a constant water activity, thus indicating that starch becomes less hygroscopic. This trend may be due to a reduction in the total number of active sites for water binding as a result of physical and/or chemical changes in the product induced by temperature (Mazza & LeMaguer, 1980). Palipane and Driscoll (1992) suggested that at increased temperatures water molecules get activated to higher energy levels, causing them to become less stable and break away from the waterbinding sites of the food material, thus decreasing the equilibrium moisture content. As temperature varies, the excitation of molecules, as well as the distance, and thus attraction between molecules, varies. This causes the amount of sorbed water to change with temperature at a given relative humidity (Mohsenin, 1986). The equilibrium moisture content of potato starch powder exhibits a stronger temperature dependence
301
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water Activity
Fig. 8. Sorption isotherms for highly amylopectin powder at 45 C.
Moisture Content (kgkg -1 DS)
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Des
Table 3 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental adsorption data for potato starch powder
Ads
0.3
Model
Constants
30 C
45 C
60 C
GAB
X0 C K E (%)
0.035 17.6 0.907 10.3
0.027 11.8 0.905 10.8
0.021 8.19 0.889 15.0
Peleg
K1 K2 n1 n2 E (%)
0.255 0.106 9.92 0.682 5.68
0.117 0.178 1.12 18.3 11.1
0.117 0.062 9.11 0.866 12.1
FerroFontan
c a r E (%)
0.022 1.08 1.26 15.9
0.014 1.07 1.29 19.3
0.020 1.13 1.06 24.3
Henderson
A B E (%)
13.8 1.07 22.6
18.6 1.07 15.4
31.0 1.12 8.11
Oswin
A B E (%)
0.069 0.390 18.8
0.052 0.390 27.2
0.037 0.380 44.4
Halsey
A B E (%)
0.473 2.23 36.3
0.266 2.23 48.8
0.096 2.33 68.7
Mod-BET
A B E (%)
0.031 0.921 30.6
0.023 0.922 38.7
0.017 0.913 53.6
Smith
A B E (%)
0.008 )0.176 9.17
0.007 )0.132 4.51
0.006 )0.090 3.49
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Fig. 9. Sorption isotherms for highly amylose powder at 45 C.
the 0:3 < aw < 0:9 region. The magnitude of the hystersis loop is smaller for highly amylopectin and highly amylose than for potato starch. Highly amylopectin and highly amylose structures are more strongly associated internally than that of potato starch. This may account for the difference in water sorption capacity, as well as the extent of the hysteresis (Van den Berg, 1981). Highly amylose starch (30% amylopectin) shows a smaller hysteresis loop than the highly amylopectin starch (99.2% amylopectin) in the range aw > 0:7. This may be due to the different structure of the starches. Both amylose and amylopectin are fully amorphous, however, due to the much easier coagulation of amylose during the separation process of amylose and amylopectin, amylose will be more strongly internally associated than amylopectin, with its branched structure (Van den Berg, 1981). The trend of the hysteresis phenomena is similar to those reported for potato by Wang and Brennan (1991), and McMinn and Magee (1999). Hysteresis is not fully understood, although there is general agreement that some thermodynamically irreversible processes must occur during desorption or adsorption, or both. The most favoured theory used to explain this thermodynamical oddity suggests that in the wet condition polar sites in the molecular structure of the material are almost entirely satisfied by adsorbed water. Upon drying and shrinkage, the molecules and their water-holding sites are drawn closely enough together to satisfy each other. This reduces the waterholding capacity of the material upon subsequent adsorption (Mohsenin, 1986). 3.3. Mathematical modelling The parameters for the sorption models for potato, highly amylopectin and highly amylose starch powders are shown in Tables 3–8, together with the mean relative percentage deviation moduli ðEÞ. Examination of the results in Tables 3 and 4 indicates that the Peleg model best describes the experimental adsorption and desorption data for potato starch
throughout the entire range of water activity. The Peleg model gives E values ranging from 5.68% to 12.4%, with average values of 9.63% for adsorption and 9.59% for desorption; this compares with average E values for the GAB model of 12.0% for adsorption and 10.1% for desorption. Peleg (1993), Rahman, Perera, and Thebaud (1998) and Delgado and Da-Wen Sun (2002) reported that the Peleg model provided a good description of the isotherms of potato starch, peas and cured beef, respectively. Van den Berg (1984), McMinn and Magee (1999) and Timmermann, Chirife, and Iglesias (2001) reported that the GAB model adequately represented the sorption isotherms of potato, wheat starch, potato and starchy materials. In the range of water activity 0:35 < aw < 0:9, the Smith model is shown to give the closest fit to the experimental data, giving an average E value of 5.72% for adsorption. Young (1976) applied the Smith model to adsorption and desorption isotherms of peanuts, and concluded that the model could be used for describing the isotherms provided that the water activity was above 0.30.
A.H. Al-Muhtaseb et al. / Journal of Food Engineering 61 (2004) 297–307 Table 4 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental desorption data for potato starch powder 60 C
303
Table 5 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental adsorption data for highly amylose powder
Model
Constants
30 C
45 C
Model
Constants
30 C
45 C
GAB
X0 C K E (%)
0.056 12.1 0.88 12.2
0.046 8.24 0.888 10.9
0.029 6.38 0.917 7.18
GAB
X0 C K E (%)
0.031 11.1 0.913 5.54
0.028 8.52 0.893 17.8
0.028 6.04 0.91 7.18
Peleg
K1 K2 n1 n2 E (%)
0.343 0.096 3.86 0.473 9.24
0.110 0.283 0.664 7.53 12.4
0.235 0.100 10.9 1.00 7.14
Peleg
K1 K2 n1 n2 E (%)
0.102 0.236 0.861 10.6 6.05
0.083 0.198 0.926 7.05 4.54
0.209 0.068 7.86 0.737 5.09
FerroFontan
c a r E (%)
0.270 1.57 0.620 13.4
0.056 1.15 0.999 16.7
0.029 1.09 1.05 15.1
FerroFontan
c a r E (%)
0.021 1.07 1.21 11.1
0.079 1.23 0.77 10.4
0.036 1.13 0.965 6.78
Henderson
A B E (%)
12.6 1.35 17.4
12.8 1.12 18.3
12.9 0.940 17.3
Henderson
A B E (%)
13.5 0.995 20.2
16.7 1.06 10.6
15.9 0.993 17.5
Oswin
A B E (%)
0.121 0.324 39.9
0.083 0.374 32.0
0.055 0.424 32.7
Oswin
A B E (%)
0.059 0.410 20.8
0.056 0.392 52.1
0.051 0.407 28.2
Halsey
A B E (%)
0.663 2.64 52.8
0.583 2.33 49.8
0.490 2.09 55.3
Halsey
A B E (%)
0.423 2.19 44.6
0.315 2.23 79.5
0.322 2.17 45.2
Mod-BET
A B E (%)
0.059 0.879 43.7
0.038 0.912 43.8
0.025 0.933 45.3
Mod-BET
A B E (%)
0.027 0.925 35.6
0.026 0.918 68.6
0.023 0.926 33.1
Smith
A B E (%)
0.047 )0.225 17.4
0.016 )0.197 12.1
)0.006 )0.168 8.64
Smith
A B E (%)
0.0002 )0.168 6.49
0.003 )0.149 6.34
)0.004 )0.146 5.41
The Halsey model least adequately represented the experimental data, giving an average E value of 51.3% for adsorption and 52.6% for desorption. Wang and Brennan (1991) reported that the Halsey model was inadequate for representing the sorption isotherms of potato, giving an average E value of 70.4%. The Henderson, Oswin and Mod-BET model failed to describe the experimental data giving an average E value above 20%. Wang and Brennan (1991) and Menkov (2000) reported that the Henderson model failed to describe the sorption isotherms of potato and lentil seeds, respectively. Examination of the results for the highly amylose starch powder (Tables 5 and 6) revealed similar observations. The Peleg model gave the best description of the experimental data with E values ranging from 4.54% to 6.20%, and an average value of 5.23% for adsorption and 6.05% for desorption. The GAB model provided a good description of the data with an average E value of 6.17% for adsorption and 4.64% for desorption. The Ferro-Fontan model gave a similar result with an average E value of 9.43% for adsorption and 5.96% for
60 C
desorption. The Smith model also adequately fitted the results with an average E value of 6.08% for adsorption and 4.10% for desorption, in the range 0:35 < aw < 0:9. Once again, the Halsey model was inadequate, giving the highest average E values of 56.4% for adsorption and 44.2% for desorption. As shown in Tables 5 and 6, other models were fitted to the experimental data. On examining the E values of the Henderson, Oswin and Mod-BET models, these were found to be unsuitable for representation of the results. In the case of highly amylopectin starch powder (Tables 7 and 8), the Ferro-Fontan model provided the best representation of the experimental data throughout the entire range of water activity, with an average E value of 7.41% for adsorption and 3.59% for desorption. Iglesias and Chirife (1995) reported that the FerroFontan equation accurately represented the sorption isotherm of 92 different food products (starches, proteins, cereals, meats, vegetables, etc.) in the range of water activity 0.1–0.9, with only 2–4% average error in the predicted moisture content. The GAB model was the
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Table 6 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental desorption data for highly amylose powder 45 C
60 C
Table 7 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental adsorption data for highly amylopectin powder
Model
Constants
30 C
Model
Constants
30 C
45 C
GAB
X0 C K E (%)
0.043 10.2 0.89 7.14
0.037 7.50 0.881 4.81
0.036 5.13 0.880 1.98
GAB
X0 C K E (%)
0.032 22.2 0.888 6.19
0.032 15.3 0.882 9.24
0.027 9.86 0.887 6.21
Peleg
K1 K2 n1 n2 E (%)
0.270 0.094 6.81 0.582 6.08
0.094 0.202 0.754 7.45 5.87
0.179 0.101 8.42 0.96 6.20
Peleg
K1 K2 n1 n2 E (%)
0.193 0.080 7.51 0.557 7.40
0.097 0.166 0.777 8.96 12.9
0.139 0.099 12.1 1.02 10.5
FerroFontan
c a r E (%)
0.046 1.14 1.06 3.53
0.045 1.16 1.00 4.37
0.050 1.18 0.932 9.98
FerroFontan
c a r E (%)
0.022 1.11 1.23 4.52
0.024 1.12 1.19 6.8
0.020 1.11 1.16 10.9
Henderson
A B E (%)
13.7 1.12 17.3
17.9 1.15 13.6
18.5 1.12 8.94
Henderson
A B E (%)
21.2 1.19 17.2
22.9 1.20 13.2
24.5 1.15 12.8
Oswin
A B E (%)
0.078 0.374 20.1
0.065 0.368 25.9
0.059 0.374 38.1
Oswin
A B E (%)
0.062 0.357 14.2
0.059 0.355 17.8
0.050 0.367 26.2
Halsey
A B E (%)
0.489 2.33 34.7
0.294 2.36 40.7
0.278 2.34 57.3
Halsey
A B E (%)
0.216 2.42 26.4
0.197 2.44 28.3
0.163 2.38 40.4
Mod-BET
A B E(%)
0.036 0.911 24.9
0.030 0.908 30.1
0.027 0.911 45.1
Mod-BET
A B E (%)
0.028 0.904 17.4
0.027 0.902 17.8
0.023 0.909 29.8
Smith
A B E (%)
0.011 )0.189 4.03
0.012 )0.151 4.06
0.010 )0.143 4.21
Smith
A B E (%)
0.016 )0.135 3.89
0.017 )0.128 2.95
0.012 )0.114 4.43
next best with an average E value of 7.24% for adsorption and 6.17% for desorption, followed by the Peleg model with an average E value of 10.27% for adsorption and 6.72% for desorption. A similar observation was found for the Smith model with an average E value of 3.76% for adsorption and 5.18% for desorption in the range 0:35 < aw < 0:9. Once again, the Halsey, Henderson, Oswin and Mod-BET models failed to adequately represent the sorption isotherms. On comparison of all the data, it can be concluded, that the Peleg, GAB and Ferro-Fontan models provide a good description of moisture sorption isotherms for all materials, at all temperatures, throughout the entire range of water activity, with the Smith model being satisfactory in the range 0:35 < aw < 0:9. The Halsey, Henderson, Oswin and Mod-BET models failed to adequately describe the experimental data for all materials in the temperature range. It should be noted that, although the Peleg and Smith models provide a good representation of the data, this is only mathematical and provides no indication of the nature of the sorption process.
60 C
3.4. Guggenheim–Anderson–de Boer model Further examination of the GAB parameters (Tables 3–8) shows that, for adsorption, the values of the monolayer moisture content, X0 are lower, and those of the Guggenheim constant C are higher than for desorption. In terms of the sorption phenomenon this means that during adsorption although less sorption sites are available, they have a greater binding energy, with the multi-layer molecules deviating more from the free bulk water (Van den Berg, 1984). Furthermore, the X0 values for all three materials show a tendency to decrease with an increase in temperature. This decrease in mono-layer moisture content can be explained by considering the structural changes in starch polymers at increased temperature. The degree of hydrogen bonding in such polymers is reduced with increasing temperature, thereby decreasing the availability of active sites for water binding and thus, the mono-layer moisture content (Westgate, Lee, & Ladisch, 1992). The Guggenheim constant was also shown to decrease with increasing temperature, indicating the ex-
A.H. Al-Muhtaseb et al. / Journal of Food Engineering 61 (2004) 297–307 Table 8 Estimated values of coefficients and mean relative percentage deviation moduli obtained for sorption models applied to experimental desorption data for highly amylopectin powder Model
Constants
30 C
45 C
GAB
X0 C K E (%)
0.041 14.59 0.902 7.58
0.041 9.13 0.881 8.06
0.034 6.79 0.89 6.09
Peleg
K1 K2 n1 n2 E (%)
0.284 0.109 8.32 0.661 8.63
0.097 0.225 0.671 7.12 7.88
0.200 0.073 6.84 0.65 3.65
FerroFontan
c a r E (%)
0.034 1.10 1.15 2.82
0.045 1.15 1.04 3.41
0.045 1.16 0.962 4.53
Henderson
A B E (%)
12.3 1.07 18.9
16.6 1.167 14.5
18.9 1.12 15.2
Oswin
A B E (%)
0.078 0.386 16.0
0.072 0.363 20.9
0.059 0.371 24.4
Halsey
A B E (%)
0.591 2.26 30.7
0.354 2.40 35.1
0.255 2.36 38.1
Mod-BET
A B E (%)
0.035 0.918 21.8
0.033 0.905 24.3
0.027 0.911 25.78
Smith
A B E (%)
0.008 )0.20 4.64
0.016 )0.164 5.53
0.009 )0.14 5.38
Table 9 Characteristic GAB parameters (Eqs. (8) and (9)) for potato starch powder c0
DHc (kJ mol1 )
k0
DHk (kJ mol1 )
0.004 0.009
21.4 18.0
0.729 1.45
0.556 )1.27
60 C
pected tendency of a decrease in binding energy for the first adsorbed layer with increasing temperature. Such a decrease indicates an increasingly shorter residence time for the adsorbed water molecules in the first layer, with the character of the adsorption process becoming less strongly localized (Calzetta Resio, Aguerre, & Suarez, 1999). A clear correlation of the constant K with temperature was not observed. Van den Berg (1984) stated that the parameters C and K incorporate the temperature effect. C is more enthalpic while K is more entropic in nature. Therefore, when describing practical isotherms over limited temperature intervals, it may suffice to incorporate the temperature effect only in C. A more detailed analysis of the GAB parameters can provide further valuable information about adsorption and desorption. A direct non-linear regression technique was adopted, with Eqs. (8) and (9) being substituted into Eq. (7). The results of the regression analysis are summarized in Tables 9–11. DHc represents the difference in enthalpy between mono-layer and multi-layer sorption (Van den Berg, 1984). The large positive value calculated is as
305
Adsorption Desorption
Table 10 Characteristic GAB parameters (Eqs. (8) and (9)) for highly amylopectin powder
Adsorption Desorption
c0
DHc (kJ mol1 )
k0
DHk (kJ mol1 )
0.003 0.003
22.6 21.5
0.825 0.723
0.188 0.545
Table 11 Characteristic GAB parameters (Eqs. (8) and (9)) for highly amylopectin powder
Adsorption Desorption
c0
DHc (kJ mol1 )
k0
DHk (kJ mol1 )
0.014 0.005
16.9 19.1
0.716 0.783
0.617 0.320
expected and is due to the strong exothermic interaction of water vapour with the primary sorption sites of starch matrix. DHk represents the difference between the heat of condensation of water and the heat of sorption of the multi-layer, which is expected to have a positive value due to the exothermic nature of moisture sorption (Van den Berg, 1984). The relatively lower magnitudes of DHk observed implies the presence of less firmly bound multilayer molecules, at intermediary energy levels between those of mono-layer molecules and the bulk liquid. The small negative value of DHk , in the case of potato starch, indicates that the heat of sorption of the multi-layer is greater than the heat of condensation of water, due to the endothermic dissolution of small molecular solutes. The DHc value for adsorption is slightly higher than the value for desorption, in the case of potato and highly amylopectin starch, and lower in the case of highly amylose starch. The variation in enthalpy values between adsorption and desorption suggests a degree of irreversibility with respect to the water binding properties of the material (McMinn & Magee, 1999).
4. Conclusions On the basis of this work the following conclusions can be drawn: • Potato starch, highly amylopectin and highly amylose powders present Type II isotherms.
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• Temperature affects the sorption behaviour; the equilibrium moisture content decreases with increasing temperature, at constant water activity. • Hysteresis is evident over the entire range of water activity for all materials. • Within the temperature range investigated, the models developed by the empirical four parameter (Peleg), the kinetic three parameter (GAB) and the semi empirical three parameter Ferro-Fontan were found to best represent the experimental data in the water activity range 0.05–0.95; the Smith model gave the best fit in the range 0.3–0.95.
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