Water desorption thermodynamic properties of pineapple

Journal of Food Engineering 80 (2007) 1293–1301 www.elsevier.com/locate/jfoodeng

Water desorption thermodynamic properties of pineapple ´ frica Castell-Palou, Carmen Rossello´ Susana Simal *, Antoni Femenia, A Department of Chemistry, University of Illes Balears, Ctra. Valldemossa km. 7.5, 07122 Palma de Mallorca, Spain Received 6 April 2006; received in revised form 3 October 2006; accepted 4 October 2006 Available online 17 November 2006

Abstract The water desorption isotherms of pineapple were determined at 5, 15, 25, 35 and 45 C by using a gravimetric technique within the water activity range of 0.1–0.9. The effect of the temperature showed a cross-over of the desorption isotherms at water activity of 0.75. The experimental data was fitted to the GAB model taking into account the effect of the temperature. The obtained simulation could be considered satisfactory (mean relative error <5.0% and percentage of explained variance >99.8%). The net isosteric heat of sorption (Qstn ) and the differential entropy (Sd) were estimated as functions of the moisture content, the enthalpy–entropy compensation theory was applied to sorption isotherms and plots of Qst vs. Sd provided the isokinetic temperature, suggesting an enthalpy controlled sorption process.  2006 Elsevier Ltd. All rights reserved. Keywords: Isotherm; Pineapple; GAB model; Isosteric heat; Entropy; Compensation theory

1. Introduction In every food product there is an inherent relationship between water content and the relative humidity of the atmosphere in equilibrium with it, which is equivalent to water activity (aw) (Mulet, Garcı´a-Pascual, Sanjua´n, & Garcı´aReverter, 2002). The thermodynamic concept of water activity (Lewicki, 2004) is used in drying applications through the sorption isotherms, which represent the change in water activity versus the change in moisture content of a sample at equilibrium and at a specified temperature. Furthermore, the knowledge of the temperature dependence of sorption phenomenon is important for modelling the thermodynamics of the system (Kumar, Singh, Patil, & Patel, 2005). Engineering design is an important application of sorption isotherms for separation process, where interface water transport is involved. Knowledge of the sorption isotherms is considered important for the design and optimization of the drying equipment, for the evaluation of

*

Corresponding author. E-mail address: [email protected] (S. Simal).

0260-8774/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2006.10.001

air–food interface state in drying process simulation and, also, to determine the drying limit at given air conditions. Several models have been proposed in the literature to mathematically describe the sorption isotherms of hygroscopic food products using isotherm equations (ASAE, 2004). Some of these models are based on theories of the mechanism of sorption; others are purely empirical or semi-empirical (Kaymak-Ertekin & Gedik, 2004). However, experience has shown that no single equation gives accurate fit for sorption isotherm data over the entire range of aw and for different types of foods (Singh, Rao, Anjaneyulu, & Patil, 2001). In general, the widely accepted criteria to select the most appropriate model are the degree of fit to the experimental data and the simplicity of the model (Kaymak-Ertekin & Gedik, 2004). Thermodynamic functions calculated from sorption isotherms allow the interpretation of the experimental results in accordance with the statement of the theory (Arslan & Togrul, 2006). The knowledge of sorption isotherms at different temperatures enables an evaluation of the heat of sorption which determines the interaction between an adsorbent and an adsorbate. A rapid computational procedure, commonly used for its determination, is the

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Nomenclature aw Cg C0 Kg K0 hm hn Lv MRE ni nw p p0 Qst Qst n

water activity Guggenheim constant entropic accommodation factor (Eq. (2)) (dimensionless) constant in the GAB model entropic accommodation factor (Eq. (3)) heat of sorption of the monolayer (kJ/mol) heat of sorption of the multilayer (kJ/mol) latent heat of vaporisation of pure water (kJ/ mol) mean relative error (%) total number of isotherms water moles (mol) partial pressure of water vapour saturation pressure isosteric heat of sorption (kJ/mol) net isosteric heat of sorption (kJ/mol)

application of the Clausius–Clayperon equation to the sorption isotherms, at constant moisture contents. The heat of sorption of water in dried foods is essential for modelling of various food processes and food storage. It can be used to estimate the energy requirements of food drying and it also provides important information on the state of water in food products (Kaya & Kahyaoglu, 2005). In general, the isosteric heat of sorption is greater than the latent heat of vaporisation of pure water at a particular temperature and can be considered as indicative of the intermolecular attraction forces between sorptive sites and water. The change in the isosteric heat of sorption with the moisture content of the sample indicates the availability of polar sites to water vapour as the desorption/adsorption proceeds (Kumar et al., 2005). The sorption processes in systems exhibiting hysteresis involve thermodynamically irreversible phenomena. Thus, the entropy production arises from this irreversibility. The changes in the entropy could be used in energy balance giving valuable information about energy utilization in food processing (Kaya & Kahyaoglu, 2005). The differential entropy of a material may be related to the number of available sorption sites at a specific energy level (McMinn & Magee, 2003). Physical phenomena, such as sorption reactions, are often evaluated on the basis of the isokinetic, or enthalpy–entropy compensation, theory. This theory (McMinn, Al-Muhtaseb, & Magee, 2005) states that compensation arises from changes in the nature of the interaction between the solute and the solvent causing the reaction, and that the relationship between enthalpy and entropy for a specific reaction is linear. When this theory is applied to a sorption process, the enthalpy corresponds to the net isosteric heat of sorption.

R Sy Syx T Ta Tb Vc Ve % var W Wm W0 DG DH

universal gas constant (kJ/mol K) standard deviation (sample) standard deviation (estimation) temperature (C) absolute temperature (K) isokinetic temperature (K) calculated value experimental value percentage of explained variance (%) moisture content (kg water/100 kg dm) monolayer moisture content (kg water/100 kg dm) constant adjusted to the temperature effect (Eq. (6)) (kg water/100 kg dm) free energy (kJ/mol) enthalpy (kJ/mol)

The concept has been successfully applied to the sorption phenomena of different foods. McMinn and Magee (2003) determined the water adsorption and desorption isotherms of potato at different temperatures (30, 45 and 60 C) and concluded that the isosteric heat versus the entropy satisfy the enthalpy–entropy compensation theory. Similarly, this theory could be successfully applied to water sorption for potatoes, macadamia nuts, apricots, figs, currants, prunes and raisins (Beristain, Garcia, & Azuara, 1996), for persimmon skin and pulp (Telis, Gabas, Menegalli, & Telis-Romero, 2000), for starch-rich materials (McMinn et al., 2005), for tea (Arslan & Togrul, 2006), among others. The objectives of this study were (i) to determine the water desorption for pineapple at different temperatures, 5, 15, 25, 35 and 45 C, (ii) model the effect of the temperature on the water desorption, (iii) determine thermodynamic functions as the isosteric heat of sorption and the differential entropy, and (iv) evaluate the applicability of the enthalpy–entropy compensation theory to the desorption phenomenon for pineapple. 2. Materials and methods 2.1. Experimental procedure Ripe pineapple fruits (Ananas comosus L. Merr) were purchased from local supermarkets, washed, peeled, and the cores removed. The total soluble solids measured as o Brix were of 13.6 ± 0.2 g/100 g. The moisture desorption isotherms for pineapple samples were determined gravimetrically using the static method of saturated salt solutions recommended by the COST 90 project (Spiess & Wolf, 1983; Rockland & Beu-

S. Simal et al. / Journal of Food Engineering 80 (2007) 1293–1301

chat, 1987). Ten saturated salt solutions selected to give different relative humidities ranging from 10% to 90% (LiCl, CH3COOK, MgCl2, K2CO3, Mg(NO3)2, NaBr, SrCl2, NaCl, KCl and BaCl2) were prepared from analytical reagent grade salts in twist-off glass containers. The glass sorption containers were placed in temperature controlled cabinet with an accuracy of ±1 C at the selected temperatures of 5, 15, 25, 35 and 45 C. Pineapple samples were exposed in the presence of the different saturated salts to give constant water activity values. After equilibrium was reached, the moisture content of the samples was determined according to the AOAC Method no. 934.06 (1990). All measurements were carried out in triplicate. The corresponding relative humidity of the salt solutions at the different temperatures was taken either from the literature (KCl, NaCl, Mg(NO3)2, K2CO3, MgCl2, CH3COOK and LiCl) (Rizvi, 1995) or experimentally measured by using an electric hygrometer NOVASINA thermoconstanter TH200 (BaCl2, SrCl2 and NaBr). The later values were in agreement with the results reported by Kiranoudis, Maroulis, Tsami, and Marinos-Kouris (1993) for the relative humidity of these saturated salt solutions at 30, 45 and 60 C. 2.2. The GAB model The most widely accepted and representative model for sorption isotherms of foods is the GAB model (Eq. (1)) (McMinn & Magee, 2003; ASAE, 2004), which according to the COST 90 study (Wolf, Spiess, & Jung, 1985) could be used to describe most food isotherms over a wide water activity range. The parameters of the GAB isotherm model have a physical meaning. In the GAB model, W is the equilibrium moisture content, the Wm parameter is the water content corresponding to saturation of all primary sites by one water molecule (namely monolayer moisture content), and Cg and Kg are energy constants. The Guggenheim constant (Cg) is related to the difference of the chemical potential in the upper layers and in the monolayer while Kg is related to this difference in the sorbate’s pure liquid state and in the upper layers. Thus, the Kg GAB parameter is, practically without exception, near but less than unity. This fact constitutes a definitive characteristic of this isotherm (Timmermann, Chirife, & Iglesias, 2001). W ¼

W m C g K g aw ð1  K g aw Þ½1 þ ðC g  1ÞK g aw 

ð1Þ

The GAB equation can describe water activity variation with temperature since Cg and Kg are exponential functions of the inverse absolute temperature (Eqs. (2) and (3))   DH 1 C g ¼ C 0 exp RT a   DH 2 K g ¼ K 0 exp RT a

ð2Þ ð3Þ

1295

The C0 and K0 parameters stand for entropic accommodation factors for the temperature effect, DH1 is the difference between the heats of sorption of the monolayer (hm) and the multilayer (hn) of water (Eq. (4)) and DH2, the difference between the heat of vaporisation of water (Lv) and the heat of sorption of the multilayer of water (hn) (Eq. (5)). DH 1 ¼ hm  hn

ð4Þ

DH 2 ¼ Lv  hn

ð5Þ

Some authors obtained for different foods that the monolayer moisture content parameter (Wm) is constant and independent of the temperature: in grapes, apricots, apples and potatoes, from 30 to 60 C (Kaymak-Ertekin & Gedik, 2004); in bitter orange leaves from 30 to 50 C (Mohamed, Kouhila, Jamali, Lahsasni, & Mahrouz, 2005); in nejayote from 25 to 60 C (Nogueira-Terrones, Herman-Lara, Garcı´a-Alvardo, & Monroy-Rivera, 2004) whereas, other authors observed that the Wm depends on the temperature according to the following relationship (Eq. (6)) where W0 is an adjusted constant (Sa´nchez, Sanjuan, Simal, & Rossello´ (1997) & McLaughlin & Magee (1998) in potato, from 4 to 50 C and from 30 to 60 C, respectively; Rahman, Perera, & Thebaud (1997) in peas from 20 to 60 C; Va´zquez, Chenlo, & Moreira (2001) in chestnut from 5 to 50 C).   DH W m ¼ W 0 exp ð6Þ RT a In the literature, some methods are recommended to determine the GAB constants. One of them is the linearization of the Eq. (1) as it is shown in Eq. (7). Thus, the representation of experimental aw/[W(1  Kgaw)] vs. aw should be linear if the correct Kg value is used (Timmermann et al., 2001) and the GAB model conforms to experimental data (Nguyen, Verboven, Daudin, & Nicolaı¨, 2004). From the two linear regression coefficients of this straight-line, the Wm and Cg constants can be obtained. aw 1 Cg  1 ¼ þ aw W ð1  K g aw Þ C g K g W m C g W m

ð7Þ

Usually, the linearization of the experimental data according to Eq. (7) is possible within the range 0.05 < aw < 0.8. At higher water activities, this representation presents a downward deviation due to the appearance of the third sorption stage being the limit of application of the GAB isotherm (Timmermann et al., 2001). However, Nguyen et al. (2004) observed in Conference pears sorption that these graphs were linear up to a certain value of aw about 0.95 and concluded that the GAB model could predict well the experimental data for aw up to 0.95. Sa´nchez et al. (1997) recommended the so-called direct method. In this method, Eqs. (2), (3) and (6) are substituted in the GAB model (Eq. (1)) and the six parameters (W0, DH, C0, DH1, K0 and DH2) are simultaneously estimated. To carry out the estimation, experimental results of water

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activity and moisture content at different temperatures are needed. Thus, the effects of both temperature and moisture content are simultaneously considered. Furthermore, the limit of Kg < 1 should be used in order to accomplish with the thermodynamic (Lewicki, 2000). The identification of the parameters of the equilibrium moisture isotherm model through the direct method was performed by using ‘‘NonLinearFit’’ of the Statistic package of Mathematica 5.2 software (Wolfram Research, Inc.), which estimates the coefficients of a nonlinear regression function, the standard errors associated to the parameters and the residuals using least squares. The percentage of variance explained by the mathematical model (% var) (Eq. (8)) (Simal, Femenia, Ca´rcel, & Rossello´, 2005) and the mean relative error (MRE) (Eq. (9)) (Nguyen et al., 2004) were used in order to evaluate the goodness of the simulation provided by the proposed model. " # S 2yx %var ¼ 1  2  100 ð8Þ Sy MRE ¼

N 100 X jV ei  V ci j N i¼1 Vei

ð9Þ

These modules have been used in the literature to evaluate the goodness of the fit for different mathematical models. It is generally accepted that MRE-values below 10% give good fit (Mulet et al., 2002; Kaymak-Ertekin & Gedik, 2004). 2.3. Thermodynamic properties

Qst ¼ Qstn þ Lv

ð13Þ

The differential entropy (Sd) can be calculated from Gibbs–Helmholtz equation (Eq. (14)) where the free Gibbs energy is calculated through Eq. (15) (Beristain et al., 1996). By substituting Eq. (15) into Eq. (14) and rearranging results Eq. (16). Qstn  DG Ta DG ¼ RT a ln aw

Sd ¼

 ln aw jnw ¼

Qstn RT a

ð14Þ ð15Þ þ

Sd R

By plotting ln(aw) vs. 1/Ta for different constant moisture contents, the Sd figure can be calculated from the y-intercept (Sd/R). According to the compensation theory, the linear relationship between enthalpy and entropy for a specific reaction is given by (Eq. (17)) Qstn ¼ T b S d þ DGb

Clausius–Clayperon equation for pure water is (Eq. (11)):   o ln p0 Lv ð11Þ ¼ oT RT 2a where p0 is the saturation pressure. Subtracting Eq. (11) from Eq. (10) (Eq. (12)):   o lnðp=p0 Þ Qst ¼ ðo ln aw =oT Þnw ¼ n2 oT RT a nw

ð12Þ

The net isosteric heat of sorption, at any value of nw, may be calculated from Eq. (12) by plotting the sorption isotherm as ln(aw) vs. 1/Ta and determining the slope which equals Qstn =R. The isosteric heat of sorption (Qst) can be calculated using Eq. (13), where Lv is the latent heat of vaporization of pure water

ð17Þ

The isokinetic temperature, Tb, represents the temperature at which all reactions in the series proceed at the same rate, and the free energy at Tb, DGb, provides a criterion to evaluate if water sorption is a spontaneous (DGb) or nonspontaneous process (+DGb). To test the validity of the compensation theory, the isokinetic temperature should be compared with the harmonic mean temperature (Thm) (Eq. (18)). Thus, a linear compensation pattern only exists if Tb 5 Thm. ni i¼1 1=T i

T hm ¼ Pni The isosteric heat of sorption is a differential molar quantity derived from the temperature dependence of the isotherm at a constant amount of sorbed water moles (nw) (Eq. (10)):   o ln p Qst ¼ ð10Þ oT nw RT 2a

ð16Þ

ð18Þ

where ni is the total number of isotherms. Moreover, if Tb > Thm the process is enthalpy driven, while if the opposite condition is observed (Tb < Thm), the process is considered to be entropy-controlled (Telis et al., 2000). 3. Results and discussion The experimental results for the equilibrium moisture content of pineapple at each water activity for the different temperatures (from 5 to 45 C) are shown in Table 1. The equilibrium moisture content at each water activity represents the mean of three replications being the standard deviation of each experimental point within the range of 0.005 and 0.09 kg/kg dry matter. As it can be observed in Table 1, for equilibrium water content ranging from ca. 0.1 to ca. 0.75, an increase in temperature promoted an increase in water activity. On the opposite, for water contents higher than ca. 0.8, an increase in temperature was followed by a decrease in water activity. These desorption isotherms which crosses as the temperature increases are typical of fruits with high sugar content (Myhara & Sablani, 2001; Nicoleti, Telis-Romero, & Telis, 2001). The solubility of sugars augments with the tempera-

S. Simal et al. / Journal of Food Engineering 80 (2007) 1293–1301

1297

Table 1 Equilibrium moisture contents (kg/100 kg dry matter) of pineapple at different temperatures T = 5 C

T = 15 C

T = 25 C

T = 35 C

T = 45 C

aw

W (% dm)

aw

W (% dm)

aw

W (% dm)

aw

W (% dm)

aw

W (% dm)

0.931 0.877 0.757 0.776 0.613 0.584 0.459 0.336 0.234 0.113

102.86 72.15 42.92 44.46 27.34 24.96 20.34 16.92 14.52 10.90

0.915 0.860 0.756 0.735 0.594 0.559 0.451 0.333 0.233 0.113

100.60 69.21 42.45 39.09 25.74 23.88 19.96 15.98 13.27 10.56

0.903 0.843 0.753 0.701 0.566 0.536 0.443 0.328 0.225 0.113

98.95 63.63 41.28 34.90 21.94 21.02 17.34 13.33 11.22 9.58

0.897 0.830 0.749 0.651 0.546 0.516 0.436 0.320 0.208 0.113

95.49 61.12 41.40 29.45 20.99 18.27 14.81 12.18 10.22 8.97

0.892 0.818 0.746 0.616 0.526 0.497 0.430 0.311 0.204 0.112

94.80 56.86 42.51 25.52 18.68 16.32 14.88 8.87 7.33 5.09

ture converting the crystalline sugar into sugar solution and thus, lowering the water activity. On the other hand, the case of water adsorption in pineapple at 20, 30, 40 and 50 C was studied by Hossain, Bala, Hossain, and Mondol (2001). These authors obtained isotherm curves which were sigmoid in shape and all curves following the same pattern, without crossings. 3.1. Fitting the GAB model to the experimental desorption data The experimental results for each temperature were fitted to a straight-line according to Eq. (7), as aw/ [W(1  Kgaw)] vs. aw. The Kg value that best linearized this fitting at every temperature (evaluated through the MRE of the predictions) was identified by using Mathematica software. Fig. 1 shows the representation of these results from 5 to 45 C and the obtained straight-lines. The other two constants, Wm and Cg, could be calculated from the slope and the y-intercept of each representation. Figures obtained for the three GAB parameters at each temperature, together with the correlation coefficients and the mean relative errors, are shown in Table 2. Although the r2 and MRE values obtained could be considered adequate, these statistical parameters indicated that the linearity of the representations was better at lower temperatures. The constants variation with the temperature was the usual

0.10

for fruits with high sugar content, thus, the Kg parameter increased with the temperature meanwhile Wm and Cg decreased. The calculated monolayer moisture (Wm) (Table 2) decreased from 11.59 kg/100 kg dm at 5 C to 9.97 kg/ 100 kg dm at 45 C. Nicoleti et al. (2001) proposed a similar trend with the temperature despite their values being very different, from 81.79 kg/100 kg dm at 40 C to 6.37 kg/100 kg dm at 70 C. However, it should be pointed out that estimated Kg figures at 35 and 45 C were higher than 1, in opposition with the physical meaning of this parameter. Similar results were obtained when the aw range was restricted to 0.05 < aw < 0.8 (results not shown) and no solution could be obtained when the estimated Kg values were limited to be lower than 1. Kaymak-Ertekin and Gedik (2004) proposed Kg values for water sorption of grapes and apricots at 45 and 60 C higher than 1. Nicoleti et al. (2001) used the GAB equation to model the water sorption of pineapple at 40, 50, 60 and 70 C. The Kg values proposed by these authors at 60 and 70 C were also higher than 1 and the variation of Cg and Kg with the temperature could not be satisfactorily fitted to the Eqs. (2) and (3), respectively. Using these results (Table 2), the Wo, DH, C0, DH1, K0 and DH2 parameters were calculated from the representation of the ln(Wm), ln(Cg) and ln(Kg) vs. the inverse of the absolute temperature. The correlations of the parameters with the temperature from 5 to 45 C are given by Eqs. (19)–(21). The corresponding linear coefficients of regression values could be considered acceptable, from

aw/[Kg(1-Kgaw)]

0.08

0.06

15ºC

Table 2 Figures obtained for the three GAB parameters at each temperature and the correlation coefficients of the straight-lines

25ºC

T (C)

Kg

Wm (% dm)

Cg

r2

MRE (%)

5 15 25 35 45

0.955 0.971 0.986 1.001 1.014

11.59 11.32 10.83 10.17 9.97

61.57 37.86 14.30 12.72 5.46

0.998 0.999 0.994 0.981 0.952

2.2 1.2 4.3 6.8 6.1

5ºC

0.04

0.02

35ºC 45ºC

0.00 0

0.2

0.4

0.6

0.8

1

aw

Fig. 1. Linear GAB plot (Eq. (7)) for pineapple at different temperatures.

S. Simal et al. / Journal of Food Engineering 80 (2007) 1293–1301

C g ¼ 4:0  107 exp

  43664:1 ; RT a



 1105:7 K g ¼ 1:541 exp ; RT a  W m ¼ 3:204 exp

r2 ¼ 0:965;

MRE ¼ 14:2%

ð19Þ r2 ¼ 0:999;

2994:6 RðT þ 273:16Þ

 ;

MRE ¼ 0:1%

ð20Þ r2 ¼ 0:970;

MRE ¼ 0:9%

ð21Þ These equations (Eqs. (19)–(21)) were used together with the GAB equation (Eq. (1)) to simulate the moisture content for different water activities and temperatures and compared with the experimental ones. The mean relative error and the percentage of explained variance obtained through this comparison were of 4.3% and 99.6%, respectively. From these results it could be concluded that the GAB model could be adequately used to represent the water desorption of pineapple from 5 to 45 C. Nevertheless, the Kg values obtained by using this method are not in agreement with the theoretical basis. As it was mentioned above, the direct method to use the GAB model consists in the simultaneous identification of the six GAB parameters by using the experimental results of moisture contents at different water activity and temperatures. To carry out the identification, figures obtained through the linearization method were used as initial values of the parameters. The statistical analysis of the non-linear regression showed that the influence of the temperature on the Wm parameter within the studied range was negligible (p < 0.05). The monolayer moisture content only varied from 11.99 kg/100 kg dm at 5 C to 11.91 kg/100 kg dm at 45 C. Thus, only five GAB parameters were simultaneous identified (Wm, C0, DH1, K0 and DH2). Results are shown in Table 3 together with the standard error associated to the estimated parameters. The Kg values obtained through the direct method varied from 0.954 at 5 C to 0.989 at 45 C, which accomplishes with the thermodynamic theory. Furthermore, it can be observed that the mean relative error (5.0%) and the percentage of explained variance (99.8%) were similar

Table 3 Parameters values of the GAB model using the direct method

Wm (kg/kg dm) C0 DH1 (J/mol) K0 DH2 (J/mol) MRE (%) = 5.0%

Estimate

Standard error

11.484 6.28 · 109 53820.6 1.276 672.1

0.18 18.5 7761.9 0.02 37.2 % var = 99.8%

to those obtained with the method of estimating Kg by the linearization of the GAB model. From DH1 and DH2 figures showed in Table 3 and Eqs. (4) and (5), the heat of sorption of the monolayer was estimated, being of 97.0 kJ/mol (the latent heat of vaporisation of water used has been of 43.9 kJ/mol, the average value within the 5–45 C range of temperature). This value is of the same order to others proposed by different authors: 90.1 kJ/mol in chestnut (Va´zquez et al., 2001); 50.6 kJ/ mol in morel (Mulet et al., 2002). Fig. 2 shows the representation of the experimental moisture content vs. the water activity for the different temperatures, from 5 to 45 C together with those simulated by using Eqs. (1)–(3) and figures of Table 3 (direct method). It can be observed the satisfactory correlation between both experimental and simulated groups of data. In order to better evaluate the goodness of the model fits, Fig. 3 shows the representation of the residuals vs. the predicted variable. 3.2. Isosteric heat of sorption and differential entropy The GAB isotherm and the parameters obtained through the direct method (Table 3) were used to estimate the net heat of sorption and the differential entropy for

120 experiment al 5º C experiment al 15º C experiment al 25º C experiment al 35º C experiment al 45º C simulat ed 5º C simulat ed 15º C simulat ed 25º C simulat ed 35º C simulat ed 45º C

100

W (% dm)

0.96 to 0.99, meanwhile the mean relative error in the case of the Cg parameter was considerably high.

80 60 40 20 0 0

0.2

0.4

0.6

0.8

1

aw

Fig. 2. Experimental equilibrium moisture data for pineapple at different temperatures (from 5 to 45 C) compared to predicted GAB isotherms using the direct method.

6

4

residuals

1298

2

0 0

25

50

75

100

-2

-4

-6

simulat ed W

Fig. 3. Representation of the residuals vs. the predicted moistures using the direct method to estimate the GAB model parameters.

S. Simal et al. / Journal of Food Engineering 80 (2007) 1293–1301

1299

5.0% 7.5% 10.0% 12.5% 15.0% 17.5% 20.0%

-1

ln(aw)

differential entropy (kJ/mol K)

0

-2

-3

-4

experiment al predict ed

0.12

0.09

0.06

0.03

0.00 0

-5 0.0031

0.0032

0.0033

0.0035

0.0034

0.0036

15

20

25

30

35

0.0037

-1

Fig. 6. Differential entropy for water desorption in pineapple as a function of the moisture content.

Fig. 4. Representation of the desorption isotherms as ln aw vs. 1/Ta for constant moisture contents. Data simulated using Eqs. (1)–(3) and figures of Table 3.

pineapple. This method requires the measurement of sorption isotherms at more than two temperatures and assumes that the thermodynamic parameters are invariant with the temperature. The water activities for certain moisture contents were simulated at different temperatures. According to Eq. (16), simulated ln(aw) was plotted vs. 1/Ta. As it can be observed in Fig. 4, good linear correlations were obtained (r2 > 0.97). The net isosteric heat of desorption and the differential entropy were calculated from the slope and the yintercept of these straight lines, respectively. The obtained figures for these thermodynamic functions (Qstn and Sd), which have been represented vs. the pineapple moisture content in Figs. 5 and 6, respectively, are of the same order than those proposed by different authors for other food products (Mohamed et al. (2005), in bitter orange leaves; Falade, Adetunji, & Aworh (2003) in fresh and osmo-dried plantain slices; Kaymak-Ertekin & Gedik (2004), in grapes, apricots, apples and potatoes; McMinn et al. (2005), in starchy materials). Different equations have been proposed in the literature to describe the variations of the net isosteric heat of desorp-

50 desorpt ion, experiment al

net heat of sorption (kJ/mol)

10

moist ure cont ent ( kg/ 100 kg dm) 1/ Ta ( K )

desorpt ion, predict ed

40

30

20

10

0 0

5

5

10

15

20

25

30

35

moist ure cont ent ( kg/ 100 kg dm)

Fig. 5. Net isosteric heat of sorption for water desorption in pineapple as a function of the moisture content.

tion of water and the differential entropy with the moisture content. Hossain et al. (2001) for the adsorption of water in pineapple (only Qstn ), and McMinn and Magee (2003) for both the adsorption and desorption of water in potato, obtained good fits by using power-law equations meanwhile Kaya and Kahyaoglu (2005) expressed the relation of the Qstn for pestil (grape leather) in the form of an exponential function and a power-law equation in the case of Sd. The mathematical relationship which better represented the results obtained in this study is shown by Eqs. (22) and (23). This form of relationship, which derives from the Ratti model (Khalloufi, Giasson, & Ratti, 2000) has been previously used by different authors (Mulet et al., 2002) to represent the variation of Qstn with the moisture content. Qstn ¼ 18:73 expð0:350W ÞW 1:684 ; S d ¼ 1:69  10

2

expð0:493W ÞW

r2 ¼ 0:997 2:804

;

2

r ¼ 0:998

ð22Þ ð23Þ

Figs. 5 and 6 also show the representation of the Eqs. (22) and (23), respectively. According to the important differences between the isosteric heat and the differential entropy and from a practical point of view, the heat involved in irreversible processes is small compared with the overall energy changes. The decrease in the net isosteric heats with the amount of water sorbed can be quantitatively explained by considering that at low moisture contents, sorption occurs on the most active available sites given rise to great interaction energy. As the moisture increases, water occupies the less active sites giving lower heats of sorption. It can be observed in Fig. 5 that the net isosteric heats (Qstn ) at low moisture contents are high, which indicates that the heat of sorption (Qstn þ Lv ) amounted twice the heat of vaporization of pure water (Lv). These initial heats may result probably from the chemisorption on polar groups. The value of Qstn was higher than zero at every moisture contents but tending to zero as the moisture content increased. Hossain et al. (2001) calculated the net isosteric heat of sorption from the adsorption isotherm of pineapple by using the modified BET model and proposed a mathematical equation of exponential shape to calculate the heat of adsorption of pineapple. This equation has been also

net heat of sorption (kJ/mol)

1300

S. Simal et al. / Journal of Food Engineering 80 (2007) 1293–1301

40

30

20

st

10

Q

n

= 342.77 Sd + 1.323 r2 = 1.000

0 0.00

0.02

0.04

0.06

0.08

0.10

0.12

dif f erent ial ent ropy ( kJ/ mol K)

Fig. 7. Net isosteric heat/entropy relation for desorption in pineapple.

represented in Fig. 5. In this case, the values of Qstn observed by these authors were low, being close to the heat of vaporization of pure water when the moisture content increase. From moisture contents of ca. 30% onwards, both curves, the proposed by Hossain et al. (2001), obtained from adsorption data, and the equation proposed in this study, obtained from desorption data, were very similar. Different authors have determined the net isosteric heat of both adsorption and desorption for some products (McLaughlin & Magee (1998) for potatoes; Kaymak-Ertekin & Gedik (2004) for grapes, apricots, apples and potatoes; Mohamed et al. (2005) for bitter orange leaves; among others). In most cases, the desorption heats were significantly higher than the adsorption ones at low moisture contents. On increasing moisture content the difference tends to disappear. This indicated that the energy required in the desorption is higher than that in the adsorption process (Kaymak-Ertekin & Gedik, 2004). Nevertheless, no definite conclusions could be drawn about the nature of the hysteresis phenomena and its relationship with the ad-desorption heat curves. The plot of Qstn vs. Sd for pineapple is shown in Fig. 7. A linear relationship was exhibited with a correlation coefficient r2 of 0.999. Thus, the results confirm the compensation theory. The isokinetic temperature (Tb) and free energy (DG), determined by linear regression were of 342.0 K and 1.67 kJ/mol, respectively. Different authors proposed isokinetic temperature values between 327 and 427.8 K for starchy food products (McMinn et al., 2005) being the DG figures positive in some products and negative in others. The calculated harmonic mean temperature was 297.5 K, value different to the isokinetic temperature value, confirming the suitability of the isokinetic theory for water sorption of pineapple. Furthermore, Tb > Thm, indicating an enthalpy controlled sorption process. 4. Conclusions The GAB model has been used to adequately represent the desorption data of pineapple at different temperatures ranging from 5 to 45 C. The two methods used to identify the model parameters allowed an accurate simulation of the experimental data (MRE < 5.0% and %var > 99.8%).

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