ARTICLES

Comparison between the isotherms of two commercial types of textured soy protein

A.S. Cassini^†, L.D.F. Marczak^† and C.P.Z. Noreña^‡

^† Chemical Engng. Department, Federal University of Rio Grande do Sul, Porto Alegre, RS, 90040-000, Brazil.
alinesc@enq.ufrgs.br, ligia@enq.ufrgs.br
^‡ Food Science and Tech. Institute, Federal University of Rio Grande do Sul, Porto Alegre, RS, 91540-000, Brazil.
czapatan@ufrgs.br

Abstract — Textured soy proteins (TSP) are functional ingredients used in food applications. This study aims to compare the sorption isotherms of two commercial types of TSP at 10, 20, 30 and 40 °C; the best fit to the experimental data was selected from eight classical models. The curves obtained for TSP type I showed that the equilibrium moisture content decreases as temperature increases for water activities up to 90%. At higher water activities, the moisture content showed an inverse behavior. This inversion did not occur for TSP type II due to the absence of sugars in this type of TSP. The Chirife, GAB and Peleg equations presented the best fit for the curves.

Keywords — Textured Soy Protein; Sorption Isotherms; Water Activity; Heat Of Sorption.

I. INTRODUCTION

Around 1950, the production of a deffated soybean flour designated to human feed were developed by the food industries due to the nutritional importance of protein and the high protein content present in the soybean (soybean contains about 40% of vegetable protein).This production increases everyday and, nowadays, more than 1.5 million ton of this defatted meal is produced worldwide. As a consequence of their great applicability in the food industry, the deffated soybean flour gave origin to three other products: textured (TSP), concentrated (CSP) and isolated (ISP) soy protein. The main difference between these three products is their protein contents: about 50%, 70% and 90% protein, respectively. The CSP and ISP are commercialized in powder, while TSP passes through an extrusion process, being commercialized under different sizes and formats.

Textured soy protein is the most widely used vegetable protein for human food processing. Generalized use of TSP in food products is due to a number of reasons, namely: increase in water and protein contents, cost reduction, texture and hardness enhancement as well as replacement of meat content while keeping the original protein content. Clearly, these advantages have been gradually augmenting the range of food products by using soy protein as a functional ingredient in their processing.

In the TSP processing, one of the main steps is the drying process, which is necessary to decrease the product moisture content to acceptable levels. The objective of dehydration in foods is to reduce the degradation caused by thriving bacteria, yeasts and molds. Moreover, undesirable chemical and biochemical reactions responsible for product degradation and shelf lifetime reduction are also heavily influenced by the moisture content. The TSP sorption isotherms are regarded as important tools in drying process operations since they describe the relationship between the relative humidity and the equilibrium moisture content of each type of TSP at constant temperatures. In general, the food industry has great interest in determining the sorption isotherms because they represent the best way to obtain data about the shelf-life and stability of its products (McLaughlin and Magee, 1998). In addition, the isotherms give relevant information concerning further steps in the process, such as packaging and storage.

Several researchers have reported sorption data for many different food products using the gravimetric static methods. McLaughlin and Magee (1998) determined the sorption isotherms for potatoes at 30, 45 and 6O°C; Prachayawarakorn et al. (2002) determined the desorption isotherms for shrimp at 50, 60, 70 and 80°C; Sandoval and Barreiro (2002) determined the water sorption isotherms of non-fermented coca beans at 25, 30 and 35°C, covering a range of a_w from 0.08 to 0.94; Mcminn et al. (2003) determined the moisture sorption isotherms of potato starch, starch-sugar and starch-salt gels at 30, 45 and 60°C, over a range of relative humidities from 0.10 to 0.84; Pahlevanzadeh and Yazdani (2005) determined the equilibrium moisture contents of powder almond at 15, 30, 55 and 75°C and of nut almond at 15, 55 and 75°C, for water activity ranging from 0.11 to 0.87; Talla et al. (2005) determined and compared the sorption isotherms of banana, mango, and pineapple at 40, 50, and 60°C for a range of water activities from 0.056 to 0.85; Wani et al. (2006) determined the moisture adsorption isotherms of watermelon seeds and kernels (two different cultivars) over a range of water activities from 0.113 to 0.92 at 20-60°C; and Furmaniak et al. (2007) adapted the Generalized D'Arcy and Watt model to the description of water vapor sorption on foodstuffs (pineapple, macaroni, sardine and pistachio nut paste) between 20 and 50°C.

Works dealing with the determination of the sorption data for soy products are, however, a little scarcer in the literature. Pan (2003) studied the adsorption characteristics of three commercial functional soy protein isolates and concentrates at different temperatures (10 - 40 °C).

The author found that the temperature is a very important factor affecting the equilibrium moisture content of these products, especially at high water activities (between 0.44 and 0.9) and that the differences in the isotherms among these three functional soy protein types are not significant. The author used the Peleg and GAB equations to fit the experimental data and both equations presented very good results. The authors did not mention the physical state of these isolates and concentrate soy protein, but it is known that these products are commercialized as a powder.

Since the use of TSP as a functional ingredient is relatively new, hardly any information on its sorption isotherms is available in the literature. The study of Cassini et al. (2006) presents the adsorption isotherms of a commercial type of TSP at 10, 20, 30 and 40°C. The authors set the experimental data to Oswin, Halsey, BET, GAB, Peleg and Darcy Watt models and found, for that type of TSP, that the equilibrium moisture content at water activities up to 0.9 decreased as the temperature increased; at higher water activities, the moisture content showed an inverse behavior, therefore resulting in a crossover of the isotherms. In addition, the monolayer moisture content of the studied type of TSP varied from 4.6% to 7.4% (db) and decreased with the increase in temperature.

This previous study encompasses a bigger one that involves the determination of drying characteristics and drying curves of different commercial types of TSP and aims to optimize the industrial drying process of these products. During the development of this project, it was necessary the determination of the sorption isotherms of a different commercial type of TSP. Therefore, the main objective of this study is to present a comparison between the sorption isotherms of a new commercial type of TSP - denominated as TSP type II, containing 70% protein and 0% sugars - and the type previously studied - denominated as TSP type I, containing 50% protein and 20% sugars - emphasizing the effect caused by the presence, or absence, of sugars in the sorption isotherms of these products. The sorption isotherms were determined under the same conditions of the previous study (temperatures of 10°C, 20°C, 30°C and 40°C) and, apart from the models tested by Cassini et al. (2006) in the experimental data fit of this study, two other models are tested.

II. THEORETICAL FUNDAMENTS

The drying process of a food product is not only responsible for changes in the moisture content but also in the water activity of this product. The drying air has a given relative humidity and, for any value attributed to it there is an equilibrium moisture content attributed to the product with this air. At this equilibrium point, the water activity of the air and the product are the same. This relationship between the equilibrium moisture content of the product and the relative humidity of drying air has great importance in the development of a drying process, since it indicates the product moisture content that can be obtained under any drying air conditions (Heldman and Hartel, 2000).

A dry product may be denominated as hygroscopic when it is capable of absorbing water concomitantly with reduction in its vapor pressure. Different products demonstrate ample variation on their hygroscopic properties due, mainly, to their molecular structure and solubility (Mujumdar, 1995). Thus, the water sorption isotherms of a product are determined in order to describe its hygroscopic properties and these curves must be determined experimentally, since food products present a very complex composition and theoretically predicted results are not reliable.

A wide variety of mathematical models to predict the water sorption isotherms of food products are available in the literature. However, as stated earlier by Labuza (1968), most of these models are only efficient in the curve prediction of certain types of food and at determined water activity intervals.

Van den Berg and Bruin (1981) pointed out more than 200 models to describe the water sorption isotherms of biological materials. The equations vary since two or three-parameters empirical models until complex thermodynamic ones. Chosen in the present work are eight mathematical models, which are among the most relevant in the prediction of the water sorption isotherms of food products. These models are presented as follows:

- Oswin (Oswin, 1946)

(1)

- Halsey (Halsey, 1948)

(2)

- BET (Barbosa-Cánovas and Vega-Mercado, 1996)

(3)

- GAB (Barbosa-Cánovas and Vega-Mercado, 1996)

(4)

- Peleg (Peleg, 1993)

(5)

- D'arcy Watt (Saravacos et al., 1986)

(6)

- Smith (Smith, 1947)

(7)

- Chirife (Castillo et al., 2003)

(8)

The heat of sorption (Q_s) is determined through the Clausius-Clapeyron equation:

(9)

where T is the absolute temperature, in K, and R_G is the universal constant of gases (R_G = 1.987 kcal/(mol.K)).

The heat of sorption can be used to estimate the total heat required during drying processes; it represents the energy required to dry the product until its monolayer moisture content. The moisture content with which the total heat of sorption approaches the heat of vaporization of pure water is often taken as an indication of 'bound' water in the foodstuff (Kaymak-Ertekin and Sultanoglu, 2001). At higher moisture contents, water is available for utilization by microorganisms as it is mechanically free in the void spaces of the system (Fasina and Sokhansanj, 1993).

The total heat of sorption (Q_st) is the sum of both the heat of sorption and the heat of vaporization of pure water (ΔH₀, assumed constant with temperature and equal to 10.53 kcal/mol):

(10)

II. METHODS

Samples of two types of TSP used in this study were obtained from commercial samples (Solae - Esteio, RS, Brazil). The initial moisture content of the samples was around 6% (wb). The geometry of these studied products was the same, but they differ from each other in their protein and sugars contents: the samples of TSP type I contained 50% protein, 20% sugars, 0% fat, 20% fibers and 4% ashes (Cassini et al., 2006) while the samples of TSP type II contained 70% protein, 0% sugars, 0% fat, 20% fibers and 4% ashes. Figure 1 presents a picture where the physical aspect of the studied types of TSP can be observed.

Fig. 1: TSP types I and II.

The curves of the equilibrium moisture content versus the water activity at 10, 20, 30, and 40 °C were obtained through the standard gravimetric method recommended by the COST 90 Project (Spiess and Wolf, 1983) using 10 saturated salt solutions -sodium hydroxide, lithium chloride, potassium acetate, magnesium chloride, potassium carbonate, potassium nitrite, sodium chloride, potassium chloride, barium chloride, and cupper sulfate - with relative humidity ranging from 7 to 97%.

Two samples of approximately 5 g of TSP were placed on a tripod above the saturated salt solution in each of 10 hygrostats (glass jars). These jars were placed inside the air-circulating thermal-isolated temperature-controlled equipment and maintained at the specified temperature within ± 0.1°C, until the equilibrium was reached (about 20 days). In order to prevent microbiological spoilage of the samples, crystalline tymol was placed in the hygrostats where high water activities occurred (a_w>0.7) (Wolf et al. 1985).

After the equilibrium had been reached, the samples were dried at 105 °C for 24 hours (AOAC, 1991) by using the oven method. Each experiment, at each temperature, was repeated once.

The fitting of experimental data to selected models and the estimation of its constants were carried out with a non-linear estimation package (Statistica '98 Edition). The regressions were repeated with various initial guessed values above and below those calculated to confirm that the regression parameters were indeed unique (Peleg, 1993).

The regression coefficient (R²) and the mean relative deviation modulus (MRD) were used to evaluate the quality of each fit. The MRD value is given in percentage and may be estimated as follows:

(11)

MRD values below 10% denote an adequate fit for practical purposes (Aguerre et al., 1989).

III. RESULTS AND DISCUSSIONS

Figure 2 shows, in the sake of comparison, the data obtained by Cassini et al. (2006) for the sorption isotherms of TSP type I; Fig. 3 shows the experimental data obtained for TSP type II at the temperatures of 10, 20, 30, and 40 °C.

Fig. 2 Water sorption isotherms of TSP type I (Cassini et al. 2006).

Fig. 3 Water sorption isotherms of TSP type II.

As can be seen in these figures, the isotherms of these two types of TSP were similar - although the curves of TSP type I have reached more elevated values of X_eq - showing a typical S-shape profile for food products: at a constant temperature, the equilibrium moisture content of the product increased with a_w. This may be due to the fact that vapor pressure of the water inside foods increases as the vapor pressure of its surrounding atmosphere increases. Moreover, all the experimental curves (for these two types of TSP) showed extremely similar results, mainly at low values of a_w. This indicates low influence of temperature (between 10 and 40 °C) in the isotherms of these types of TSP. This result disagrees; however, with Pan (2003), since the author found a significant influence of temperature in the isotherms of two isolates and one concentrate soy products. This disagreement is probably due to the physical format and, also, due to the protein content of the products.

After the determination of the experimental curves, the equilibrium moisture content versus the water activity data of TSP type II were fit to the mathematical models presented earlier.

Through the fit results it was possible to observe that some models presented satisfactory fit to the experimental data, while others could not be used in the prediction of water sorption isotherms of this type of TSP, within the range of temperature studied. Considering the correlation coefficient, most of the models presented values very close to the unity, thus indicating the good fit of the proposed models to the experimental data; considering, however, the MRD value, it was observed that just few models fit satisfactorily (MRD values below 10%).

Table 1 shows the results of the best fittings obtained for TSP type II, that is, the estimated constants, the correlation coefficient and the mean relative deviation modulus generated by the fitting of Peleg, GAB and Chirife models to the experimental data.

Table 1: Best fittings results for TSP type II.

As illustrated by this table, the best model capable to predict the sorption isotherms of TSP type II between 10 and 40°C is the Peleg model, since the MRD values generated were the lowest observed. The Chirife and GAB models, however, can certainly be used in the prediction of these curves as well, since the estimated MRD values were below 10%. Pan (2003) obtained good results using GAB and Peleg models to fit the isotherms of two types of isolates and one type of concentrate soy protein.

According to Cassini et al. (2006), the best fits for TSP type I were obtained by the GAB and Peleg models: the first presented the lowest MRD value for higher temperatures (30 and 40 °C) and the latter, for lower temperatures (10 and 20 °C). The GAB model, however, was the only one capable to show the crossing of the TSP type I isotherms. This phenomenon will be discussed further.

Since the Chirife model has fit well with the experimental data of TSP type II - even better than the GAB model - and since it had not been used in the work of Cassini et al. (2006), this model was tested in the prediction of TSP type I curves. The results are presented in Table 2, which also contains, for the sake of comparison, the results obtained by Cassini et al. (2006) with the GAB model.

Table 2: Fitting of TSP type I experimental data to Chirife and GAB (Cassini et al. 2006) models.

As can be seen in this table, the model of Chirife also presents very good results in the prediction of the sorption isotherms of TSP type I between 20 and 40°C. Only at the lowest temperature, the MRD value generated was slightly greater than 10%. Comparing the MRD values generated by the fitting of TSP type I experimental data to the GAB and Chirife models, it can be visualized the better result obtained by the Chirife model.

Besides these two models, other ones, like Halsey, Oswin and D'arcy Watt, also generated good results at determined temperatures. The Halsey model, for instance, showed a better result in fitting TSP type I data than TSP type II, generating low MRD values in the fitting of TSP type I experimental data at higher temperatures (30 and 40 °C). Since protein content of TSP type II is greater than TSP type I, this result disagrees with Iglesias and Chirife (1976), which indicated the good fit of the Halsey model to the isotherms of high protein content foods.

In the same way, the fitting of the TSP type II experimental data to the D'arcy Watt model generated low MRD values at three temperatures (10, 20, and 40°C), but just for one temperature for TSP type I. Since the sugar content of TSP type I and II is, respectively, 20 and 0%, this result opposes the results of Saravacos et al. (1986), which indicated a better fit of this model to the isotherms of high sugar content foods.

In order to observe clearly the sorption behavior of these two types of TSP, Fig. 4 and Fig. 5 present the fitting of the sorption isotherms of TSP type I and II, respectively, at 20 and 40 °C, to the Chirife model. In this figure, the legends exp and calc refer, respectively, to experimental data and calculated values.

Fig. 4 Fitting of TSP type I sorption isotherms (20 and 40°C) to Chirife model.

Fig. 5 Fitting of TSP type II sorption isotherms (20 and 40°C) to Chirife model.

These figures show, as stated earlier, that the isotherms of each type of TSP (at different temperatures) were very similar, showing little influence of temperature variation (between 20 and 40°C). However, an important difference between the curves obtained for TSP type I and II is observed: under constant a_w, the curves of TSP type I (Fig. 4) clearly show an inversion of their behavior, which did not occur with the curves of TSP type II (Fig. 5).

As can be seen in Fig. 4, the TSP type I sorption isotherm at 40 °C crosses the TSP type I sorption isotherm at 20°C at a a_w value around 0.9. This phenomenon is characteristic of high sugar content foods. Labuza (1984) found that the inversion in the behavior of isotherms is caused by microbiological growth and/or the dissolutions of sugars (the higher the temperature, the higher the dissolution of sugars and, consequently, the higher the equilibrium moisture content of the sample).

Different studies reported the crossing of isotherms for various types of sugar-containing foods. Tsami et al. (1990) determined the sorption isotherms of some dried fruits between 15 and 60°C. The authors founded that the higher was the sugar content of the product, the lower was the value of a_w in which this crossing occurs. Thus, the crossing of the isotherms in a high value of a_w (around 0.9) was expected since the sugar content of TSP is about 20%. According to the study of Cassini et al. (2006), the visualization of the crossing of the isotherms was possible by means of the GAB model; it means that the fit with this model was so good that the crossing of the isotherms could be observed. On the other hand, the fit with Peleg model was not able to show this same behavior.

In Fig. 5 it can be observed that the TSP type II curves come pretty close to one another, but the crossing does not occur in any moment. This result agrees with Benado and Rizvi (1985), apud Tsami et al. (1990), which indicated the absence of crossings at isotherms of high protein content foods.

Therefore, the Chirife model can be indicated as the most suitable model for the prediction of these curves between 20 and 40°C since it was not only the best one in predicting sorption isotherms of these two types of TSP but also one that is able to show the crossing of the TSP type I isotherms. As stated earlier, nonetheless, the GAB model is also very useful since it provides, directly, the monolayer moisture content of the products presented as well as partially good results in the fitting of the studied data.

Table 3 presents the TSP types I (Cassini et al. 2006) and II monolayer moisture content values, estimated through fitting the experimental data to the GAB model, at 10, 20, 30, and 40°C.

Table 3: Monolayer moisture content (db) of TSP types I (Cassini et al., 2006) and II.

It can be seen from this table that the monolayer moisture content values of both types of TSP diminished as temperature increased. The observed behavior agrees with the results obtained by several authors - McLaughlin and Magee (1998), Kaymak-Ertekin and Sultanoglu (2001), Iglesias and Chirife (1976), Labuza et al. (1985), Wang and Brennan (1991). In addition, all the estimated values are within the limit monolayer moisture content of 10% (0.1 kg water/kg db), stated earlier by Labuza et al. (1985), for food products. The monolayer moisture content obtained by Pan (2003) for a commercial type of ISP (0.1006 kg water/kg db) was a little bigger than the one obtained by the present work for the TSP.

The total heat of sorption was also estimated for both types of TSP through the Clausius-Clapeyron equation and fitting experimental data to Chirife model. Figure 6 presents the total heat of sorption of each type of TSP as a function of their equilibrium moisture content.

Fig. 6: Total heat of sorption (kcal/mol) of TSP types I and II.

As shown in this figure the total heat of sorption of both types of TSP decreased as the moisture content increased. This behavior was already expected, since the lower the moisture content, the more energy to remove this water from inside the product is needed.

When comparing two types of TSP, it can be observed that TSP type II demands a greater quantity of energy to reduce its moisture content than does TSP type I, especially in the regions with low (< 0.12 kg water/kg db) and high (> 0.30 kg water/kg db) equilibrium moisture content. In addition, the total heat of sorption of TSP type I approximates to that of pure water value (10.53 kcal/mol) at a moisture content around 30% (db) against 40% of TSP type II. Beyond this value, water found in TSP might not be in a bound form but existing as mono or multi-layer, being, probably, available for utilization by microorganisms (Iglesias and Chirife, 1976).

By using the Chirife model, lower values of TSP type I total heat of sorption were obtained, when comparing to data from Cassini et al. (2006) - which estimate the total heat of sorption of TSP type I using the GAB model - mainly above the pure water value (10.53 kcal/mol). The Q_s value that approximates to the pure water value, however, is very close to that estimated by GAB (28%).

III. CONCLUSIONS

This work dealt with the determination of the sorption isotherms of two commercial types of textured soy protein (TSP). The emphasis was to compare the TSP type I water sorption isotherms, previously determined by Cassini et al. (2006) at four different temperatures (10, 20, 30, and 40 °C), with the curves obtained for TSP type II, focusing on the behavior of the obtained curves (based on the presence or absence of sugars), on the fit quality of the studied models and on the different parameters obtained from these sorption isotherms.

The curves obtained for each type of TSP were very similar, indicating low influence of temperature in the equilibrium moisture content as a function of the water activity of TSP type I and II; the curves of TSP type I have reached more elevated values of X_eq than the TSP type II curves.

TSP type II isotherms presented the same behavior for any water activity value; TSP type I isotherms, however, showed an inverse behavior at a water activity value around 0.9, due to their sugar content.

The Chirife, GAB and Peleg models presented the best fit to the experimental data of both types of TSP, but, for TSP type I, just Chirife and GAB were capable to show the crossing of its isotherms, due to their excellent fit to the isotherms at each particular temperature.

The total heat of sorption of TSP type I and II was also estimated; this parameter increased as their equilibrium moisture content decreased and it was observed that TSP type II demanded a higher quantity of energy to reduce its moisture content than did TSP type I.

REFERENCES

1. Aguerre, R.J., C. Suarez and P.Z. Viollaz, "New BET type multi-layer sorption isotherms. Part II: Modelling water sorption in foods," Leb.-Wiss. Tech., 22, 192-195 (1989).         [ Links ]

2. AOAC, Association of Official Analytical Chemists. Official Methods of Analysis, AOAC, New York (1991).         [ Links ]

3. Barbosa-Cánovas, G.V. and H. Vega-Mercado, Dehydration of Foods,. Chapman-Hall, New York (1996).         [ Links ]

4. Benado, A.L. and S.S.H. Rizvi, "Thermodynamics properties of water on rice as calculated from reversible and irreversible isotherms," J. Food Sci., 50, 101-105 (1985).         [ Links ]

5. Cassini, A.S., L.D.F. Marczak and C.P.Z. Noreña, "Water adsorption isotherms of texturized soy protein," J. Food Eng., 77, 194-199 (2006).         [ Links ]

6. Castillo, M.D., E.J. Martínez, H.H.L. González, A.M. Pacim and S.L. Resnik, "Study of mathematical models applied to sorption isotherms of Argentinean black bean varieties," J. Food Eng., 60, 343-348 (2003).         [ Links ]

7. Fasina, O.O. and S. Sokhansanj, "Equilibrium moisture relations and heat of sorption of Alfafa Pellets," J. Agric. Eng. Res., 56, 51-63 (1993).         [ Links ]

8. Furmaniak, S., A.P. Terzyk, P.A. Gauden and G. Rychlicki, "Applicability of the generalised D'Arcy and Watt model to description of water sorption on pineapple and other foodstuffs," J. Food Eng., 79, 718-723 (2007).         [ Links ]
9. Halsey, G, "Physical Adsorption on Non-uniform Surfaces," J. Chem. Phys., 16, 931-937 (1948).         [ Links ]

10. Heldman, D.R. and R.W. Hartel, Principles of Food Processing, Chapman & Hall, New York (2000).         [ Links ]

11. Iglesias, H.A. and J. Chirife, "BET monolayer in dehydrated foods and food components," Leb.-Wiss. Tech., 9, 107-113 (1976).         [ Links ]

12. Kaymak-Ertekin, F. and M. Sultanoglu, "Moisture sorption isotherm characteristics of peppers," J. Food Eng., 47, 225-231 (2001).         [ Links ]

13. Labuza, T.P. "Sorption phenomena in foods," Food Tech. II, 22, 263-272 (1968).         [ Links ]

14. Labuza, T.P. Moisture sorption: practical aspects of isotherm measurement and use, American Association of Cereal Chemists (1984).         [ Links ]

15. Labuza, T.P., A. Kaanane and J.Y. Chen, "Effects of temperature on the moisture sorption isotherms and water activity shift of two dehydrated foods," J. Food Sci., 50, 385-392 (1985).         [ Links ]

16. McLaughlin, C.P. and T.R.A. Magee, "The determination of sorption isotherm and the isosteric heats of sorption for potatoes," J. Food Eng., 35, 267-280 (1998).         [ Links ]

17. Mcminn, W.A.M., A.H. Al-Muhtaseb and T.R.A. Magee, "Moisture sorption characteristics of starch gels. Part I: mathematical description of experimental data," J. Food Proc. Eng., 26, 323-338 (2003).         [ Links ]

18. Mujumdar, A.S., Handbook of Industrial Drying. Second Edition, V. 1. Marcel Dekker, Inc., New York (1995).         [ Links ]

19. Oswin, C.R., "The kinetics of Package Life III: The Isotherm," J. of Chem. Ind., 65, 419-421 (1946).         [ Links ]

20. Pahlevanzadeh, H. and M. Yazdani, "Moisture adsorption isotherms and isosteric energy for almond," J. Food Proc. Eng., 28, 331-345 (2005).         [ Links ]

21. Pan, Z., "Adsorption characteristics of functional soy protein products," J. Food Proc. Eng., 25, 499-514 (2003).         [ Links ]

22. Peleg, M., "Assessment of a semi empirical four parameter general model for sigmoid moisture sorption isotherms," J. Food Proc. Eng., 16, 21-37 (1993).         [ Links ]

23. Prachayawarakorn, S., S. Soponronnarit, S. Wetchacama and D. Jaisut, "Desorption isotherms and drying characteristics of shrimp in superheated steam and hot air," Dry. Tech., 20, 669-684 (2002).         [ Links ]

24. Sandoval, A.J. and J.A. Barreiro, "Water sorption isotherms of non-fermented cocoa beans," J. Food Eng., 51, 119-123 (2002).         [ Links ]

25. Saravacos, G.D., D.A. Tsiourvas and E. Tsami, "Effect of temperature on the water adsorption isotherms of sultana raisins," J. Food Sci., 51, 381-383 (1986).         [ Links ]

26. Smith, S.E., "The sorption of water vapour by high polymers," J. Am. Chem. Soc., 69, 646-651 (1947).         [ Links ]

27. Spiess, W.E.L. and W.F. Wolf, The results of the COST 90 project on water activity. Physical Properties of Foods, Applied Science Publishers, London (1983).         [ Links ]

28. Talla, A., Y. Jannot, G.E. Nkeng and J.R. Puiggali, "Experimental determination and modeling of sorption isotherms of tropical fruits: banana, mango, and pineapple," Dry. Tech., 23, 1477-1498 (2005).         [ Links ]

29. Tsami, E., D. Marinos-Kouris and Z.B. Maroulis, "Water sorption isotherms of raisins, currants, figs, prunes and apricots," J. Food Sci., 55, 1594-1597 (1990).         [ Links ]

30. van den Berg, C. and S. Bruin, "Water Activity and its Estimation in Food Systems: Theoretical Aspects," In Water Activity: Influences of Food Quality, Ed. Rockland and Stewart, New York (1981).         [ Links ]

31. Wang, N. and J.G. Brennan, "Moisture sorption isotherm characteristics of potatoes at four temperatures," J. Food Eng., 14, 269-287 (1991).         [ Links ]

32. Wani, A.A., D.S. Sogi, U.S. Shivhare, I. Ahmed and D. Kaur, "Moisture adsorptions isotherms of watermelon seed and kernels," Dry. Tech., 24, 99-104 (2006).         [ Links ]

33. Wolf, W., W.E.L. Spiess and G. Jung, Standardization of isotherms measurements (cost-project 90 and 90 bis). Properties of water in foods in relation to quality and stability. Martinus Nijhoff Publishers, Dordrecht (1985).         [ Links ]

Received: January 17, 2008.
Accepted: May 19, 2008.
Recommended by Subject Editor: Ricardo Gómez.