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Journal of Stored Products Research 43 (2007) 252–264 www.elsevier.com/locate/jspr

Moisture sorption isotherms and thermodynamic properties of walnut kernels Hasan Tog˘rul, Nurhan Arslan Department of Chemical Engineering, Faculty of Engineering, Fırat University, 23279 Elazıg˘, Turkey Accepted 26 June 2006

Abstract The moisture sorption isotherm data of walnut kernels stored in a chamber, the relative humidity (r.h.) of which is regulated by atomizing humidiﬁer, were determined at three different temperatures (25, 35 and 45 1C) and r.h. ranging from 10% to 90%. Eight models, namely the GAB, BET, Henderson, Iglesias and Chirife, Oswin, Peleg, Smith and Caurie equations, were ﬁtted to the sorption data. Several statistical tests were adopted as the criteria to evaluate the ﬁtting performance of the models. Of the models tested, the Peleg model gave the best ﬁt to experimental data. The surface area of a monolayer was calculated. The BET equation was applied to the monolayer moisture content and the corresponding aw values at which a monolayer forms are presented. The experimental data were also used to determine the thermodynamic functions such as isosteric heat of sorption, sorption entropy, spreading pressure, net integral enthalpy and entropy. The sorption isosteric heats for walnut kernels were determined by the application of the Clausius–Clapeyron equation to sorption isotherms obtained from the best-ﬁtting equation. Isosteric heats decreased with increase in moisture content and approached the latent heat of pure water. Adsorption entropy increased with increasing moisture content, and then it decreased sharply with increase in moisture content. The spreading pressures (adsorption and desorption) increased with increasing water activity. Net integral enthalpy of adsorption increased slightly with moisture content to a maximum value. Thereafter, it remained constant. Net integral entropy of adsorption was negative in value and it decreased with increase in moisture content to a minimum value, and then increased slightly with increase in moisture content. r 2006 Elsevier Ltd. All rights reserved. Keywords: Walnut kernels; Moisture sorption; Isotherms; Thermodynamic; Atomizing humidiﬁer

1. Introduction Turkey is an internationally important walnut producer with a production of 136,000 tonnes in 2003, representing 9.6% of the total world market (FAO, 2003). Water sorption is one of the most important parameters that contribute to predicting technological performance and product quality in stored foods (Chirife and Buera, 1994). The long-term storage of a product containing water, sugar, fat and protein causes deteriorative reactions such as browning, lipid oxidation and microbial growth. Inﬂuence of moisture on these reactions has been explained in terms of water activity (aw), and this approach is now well Corresponding author. Tel.: +90 424 2370000; fax: +90 424 2415526.

E-mail address: [email protected]ﬁrat.edu.tr (N. Arslan). 0022-474X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jspr.2006.06.006

established in controlling reactions and predicting food stability (Nelson and Labuza, 1994). The relationship between water activity and moisture content is explained by means of moisture sorption isotherms. Food moisture isotherms and the equations that describe this relationship are important in equipment design for drying, packaging and storage, for prediction of shelf-life, and for determination of critical moisture and water activity for acceptability of products that deteriorate mainly by moisture gain (Van den Berg and Bruin, 1981; Palou et al., 1997). According to thin-layer kinetics, the drying ranges are 0–80% relative humidity (r.h.) and 20–80 1C (Courtois et al., 2001). Many empirical and semi-empirical equations describing the sorption characteristics are suitable for some food products only, or for selected ranges of water activity, and

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Nomenclature a, b aw (aw)x (aw)* A, B Am Ax, Bx b, b0

c 1, c 2 C C0 eave E DH c DH k

K K0

Caurie and Iglesias–Chirife model parameters water activity water activity corresponding to the monolayer moisture content geometric mean water activity at constant spreading pressure Henderson and Oswin model parameters area of a water molecule (1.06 1019 m2 molecule1) constants of Eq. (8) constants from Dent sorption isotherm related to the properties of the adsorbed water (dimensionless) Smith model parameters GAB and BET model parameter constant (adjusted to the temperature effect) (dimensionless) average residual mean relative percentage deviation modulus (%) difference in enthalpy between monolayer and multi-layer sorption (J mol1) difference between the latent heat of vaporization of pure water and heat of sorption of the multi-layer (J mol1) GAB model parameter constant (adjusted to the temperature effect) (dimensionless)

parts of these equations reﬂect the effect of temperature on sorption isotherms Chirife and Iglesias (1978) reviewed some of these models and reported 23 common equations for ﬁtting sorption isotherms to different food materials. Some models take into account the effect of temperature, among them are the modiﬁed Chung–Pfost (Chung and Pfost, 1967), modiﬁed Henderson (Henderson, 1952), modiﬁed Halsey (Halsey, 1948) and modiﬁed Oswin (Oswin, 1946) models. The equations of Brunauer– Emmett–Teller (BET) and Guggenheim–Anderson–de Boer (GAB) appear to be the most popular food isotherm equations (Cadden, 1988). Further analysis of sorption isotherm data by application of thermodynamic principles can provide much important information regarding the dehydration process energy requirements, food microstructure and physical phenomena on the food surfaces, water properties and sorption kinetic parameters (Rizvi and Benado, 1984). Isosteric heat of sorption, often referred to as differential heat of sorption, is used as an indicator of the state of water adsorbed by the solid particles (Fasina et al., 1997). Knowledge of the differential heat of sorption is of great importance when designing equipment for dehydration processes. The net isosteric heat is useful in estimating the state of adsorbed water by solid particles, which is a

253

Boltzmann’s constant (1.380 1023 J K1) Peleg model parameters molecular weight of water (18 kg kgmol1) Peleg model parameters number of experimental data Avogadro’s number (6 1026 molecules kgmol1) latent heat of vaporization of pure water (kJ mol1) heat of sorption of the ﬁrst layer (kJ mol1) heat of sorption of a multi-layer (kJ mol1) isosteric heat of sorption (kJ mol1) net isosteric heat of sorption (kJ mol1) net integral enthalpy (kJ mol1) universal gas constant (8.314 J mol1 K1) or the standardized residual RMSE root mean square error S solid surface area (m2 g solids1) DS sorption entropy (J mol 1 K1) DS in net integral entropy (J mol1 K1) t temperature (1C) T temperature (K) X equilibrium moisture content (% d.b.) X0.5 equilibrium moisture content at aw 0.5 (% d.b.) Xei experimental value of equilibrium moisture content (% d.b.) Xm monolayer moisture content (% d.b.) Xpi predicted value of equilibrium moisture content (% d.b.) f spreading pressure (J m2) y moisture ratio

KB m1, m2 Mwat n1, n2 N NA qc qm qn Qst Qst n Qin R

measure of the physical, chemical and microbial stability of food in storage (Labuza, 1968). The net integral enthalpy or net equilibrium heat of sorption provides a measure of the strength of moisture–solid binding (Fasina et al., 1999). The differential entropy of a material is proportional to the number of available sorption sites at a speciﬁc energy level. Integral entropy describes the degree of disorder of water molecules (Al-Muhtaseb et al., 2004b). Thermodynamic parameters such as differential enthalpy and entropy, and integral enthalpy and entropy determine the end-point to which food must be dehydrated in order to achieve a stable product with optimal moisture content, and yield the theoretical minimum amount of energy required to remove a given amount of water from the food. These parameters also provide an insight into the microstructure associated with the food as well as the theoretical interpretation of physical phenomena occurring at the food–water interface (Rizvi, 1986). For various types of foods, research on the temperature dependence of isotherms, mathematical models to represent sorption isotherms and determination of heat of sorption have been reported in the literature (Sood and Heldman, 1974; Singh and Lund, 1984; Palou et al., 1997; Ajibola et al., 2003). Lopez et al. (1998) determined the moisture sorption characteristics of three different varieties

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of walnut kernels at 3, 10 and 30 1C, and stated that the BET and GAB models gave the minimum mean square error. Lavialle et al. (1997) determined the sorption curves of four constitutive parts of the whole walnut. Lopez et al. (1995) stated that the cold storage of unshelled walnuts at 40% r.h. caused a signiﬁcant weight loss of dehydration. Data on the moisture sorption isotherms of walnut kernels stored in a chamber, the r.h. of which is regulated by an atomizing humidiﬁer, would be helpful for evaluation of keeping quality and packaging requirements under varying humidity conditions. The objectives of this study were to determine experimentally the equilibrium sorption isotherms of walnut kernels at different temperatures, to select the most suitable model describing the isotherms, to determine the water activities corresponding to the monolayer moisture content being invariant with temperature and to determine isosteric heat of sorption, net integral enthalpy, sorption entropy and net integral entropy for the sorption isotherms of walnut kernels. 2. Materials and methods 2.1. Description of experimental procedure Unshelled walnuts (Juglans regia L.) cultivated in the Elazıg˘ district of Turkey were procured from a local market. The shells were cracked and the kernels were removed. The walnut kernels were cut into 1 cm cubes. Sorption isotherms of the walnut kernels without surface layers were determined. The initial moisture of walnut kernels was determined as 3.6270.1% on a wet basis by drying in an air-oven to constant weights at 105 1C. The

walnut kernels contained 9.75% w.b. carbohydrate, 20.93% w.b. protein and 63.9% w.b. fat (for all analyses, n ¼ 2, S.D. ¼ o0.057%). The temperature and r.h.-controlled chamber was constructed from Cr–Ni stainless-steel sheets as a rectangular box of size 95 124 200 cm3. All sides and the platform of the chamber were insulated (Fig. 1). The equilibrium moisture content (EMC) of walnut kernels was determined in the range of 10–90% r.h. and the effect of temperature was investigated using three temperatures; 25, 35, 45 1C. Initially, silica gel (Crosﬁeld Chemicals, UK) was used to obtain 10% r.h. in the chamber. For the adsorption process, the temperature in the chamber was adjusted to the value desired and the dried samples of nearly 8 g in specimen baskets of stainless-steel wire were placed in the humidity- and temperature-controlled chamber. The humidity in the chamber was controlled by an atomizing humidiﬁcation system for levels above 10% r.h. Water puriﬁed by a water treatment system consisting of an ion exchanger and reverse osmosis system was stored in a tank of 200 l capacity. Treated water was pumped to the chamber and was adjusted to a pressure of 4 bar by a water pressure regulator. Compressed air was passed through an air ﬁlter at 4.5–7 bar, and was regulated to a pressure of 4 bar by the air pressure regulator of the atomizer. Water and air were fed to an atomizing Venturi nozzle. The compressed air constantly drew water from the reservoir and created a fog which was shot into the chamber to raise the humidity. Dry air heaters of 3 kW and a cooling heat pump were used to heat or cool the chamber, respectively. The temperature and r.h. were kept at constant values by calibrated temperature and r.h. controllers. Temperature was monitored by means of a

Fig. 1. Schematic diagram of the experimental apparatus (1, water inlet; 2, pump; 3, air pressure tank; 4, ﬁlter; 5, ion exchanger; 6, membrane; 7, drainage; 8, puriﬁed water; 9, water tank; 10, pump; 11, valve; 12, water valve; 13, no return valve; 14, water pressure regulator with manometer; 15, water valve (opening by air pressure); 16, compressor; 17, air ﬁlter; 18, air pressure regulator; 19, electric valve; 20, air valve with manometer; 21, ﬁtting; 22, atomizing nozzle; 23, temperature sensors; 24, percent relative humidity probe ; 25, fan; 26, specimen baskets; 27, UV lamp; 28, hermetic compressor; 29, condenser; 30, liquid tank; 31, ﬁlter drier; 32, solenoid valve; 33, thermostatic expansion valve; 34, evaporator; 35, dry air heater; 36, temperature and relative humidity control panel; 37, cooling unit; 38, constant temperature and humidity chamber).

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platinum resistance thermometer. A r.h. (%) monitoring device was operated by means of a humidity probe, the sensor elements of which were coated with an electrostatic capacitance type high polymer ﬁlm. The r.h. sensor (RH31, Omega Engineering Inc., USA) was calibrated with a saturated salt solution of lithium chloride (to simulate 11% r.h.) and a saturated salt solution of sodium chloride (to simulate 75% r.h.). A radial fan circulating the vaporized water inside chamber was used to reduce equilibrium time. An UV lamp (Philips, TUV G30T8, Holland) of 30 W was used to inhibit fungal activity. An uninterruptible power supply of 3000 VA (Inform, Guard 1600, Turkey) was used to secure electrical protection. In adsorption experiments, two samples were withdrawn for weighing on an electronic balance with an accuracy of 0.001 g (Shimadzu Corporation, BX 300, Japan) at regular intervals until they had reached constant mass (70.001). The total time required for removal, weighing and replacing the samples in the chamber was approximately 15 s. This minimized the degree of atmospheric moisture sorption during weighing. The moisture content was calculated from the increase in mass of the dried sample after reaching equilibrium at a given r.h. EMC of the samples was expressed as % dry basis (% d.b). The water activity was calculated as % r.h./100. Adsorption processes were repeated for the range of 10–90% r.h. in the order of increasing r.h.. For the desorption process, samples were held at 97% r.h. until equilibrium was reached. Silica gel was used to lower r.h. levels to 90% and then in 10% steps down to 10% r.h. to cover the full experimental range. In desorption experiments, samples were weighed to determine weight loss and the equilibrium was judged to have attained when the difference of three consecutive weighings did not exceed 2 mg. Sorption processes were repeated for temperatures of 25, 35 and 45 1C71. Experiments were run twice at each temperature. The mean values were used for the adsorption and desorption isotherm determination. The mean of standard deviations of the ﬁnal moisture contents was 0.003 g. The equilibrium period ranged from 4 to 17 days, depending on the temperature and r.h. As expected, the higher the temperature the shorter the equilibrium time, and the higher the r.h. the larger the equilibration time.

255

2.2. Data analysis and determination of thermodynamic functions 2.2.1. Sorption isotherm equations In this study, the eight models were applied to ﬁt the adsorption data for walnut kernels and models are represented in Table 1. X, Xm, aw and X0.5 in Table 1 are EMC, monolayer moisture content, water activity and EMC at the aw of 0.5, respectively. The other symbols are the model constants. A nonlinear estimation package (Statistica, 1995) was used to estimate the constants of the equilibrium moisture models within the range of 0.1–0.9 water activity. The goodness-of-ﬁt of different models was evaluated with the mean relative deviation (E %), the average residuals and the root mean square error (RMSE) between the experimental and predicted EMC, as deﬁned by Iglesias and Chirife (1976a): n X ei X pi 100 X E%¼ , (1) n i¼1 X ei eave ¼

n X ðX ei X pi Þ=n,

(2)

i¼1

"

n 2 1X RMSE ¼ X ei X pi n i¼1

#1=2 ,

(3)

where Xei is the experimental value, Xpi the predicted value, eave the average residual and n the number of observations. The ﬁt of a model is good enough for practical purposes when E % is less than 10% (Aguerre et al., 1989). In the GAB model, Xm is the moisture content corresponding to formation of a monomolecular layer on the internal surface, C a constant related to the heat of sorption of the ﬁrst layer on primary sites and K a factor correcting properties of the multi-layer molecules with respect to the bulk liquid. C and K constants in the GAB equation were correlated with temperature by using the following Arrhenius-type equations (Sanni et al., 1997): C ¼ C 0 exp ½ðqm qn Þ=RT,

(4)

K ¼ K 0 exp ½ðqc qn Þ=RT,

(5)

Table 1 Moisture sorption models used Name of model

Model

GAB (Van den Berg and Bruin, 1981) BET (Brunauer et al.,1938) Henderson (Henderson, 1952) Iglesias and Chirife (Chirife and Iglesias, 1978) Oswin (Oswin, 1946) Peleg (Peleg, 1993) Smith (Smith, 1947) Caurie (Caurie, 1970)

X ¼ XmCKaw/[(1-Kaw)(1-Kaw+CKaw)] X ¼ XmCaw/[(1-aw)(1-aw+Caw)] X ¼ [ln(1aw)/A]1/B ln[X+(X2+X0.5)1/2] ¼ a+baw X ¼ A[aw/(1aw)]B n2 X ¼ m1an1 w +m2aw X ¼ c1–c2 ln(1aw) X ¼ exp(a+baw)

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where C0 and K0 are constants, qm (kJ mol1) is the sorption heat of the monolayer absorbed water, qn (kJ mol1) is the of sorption heat of the nth multi-layer absorbed water, qc (kJ mol1) is the heat of condensation of water vapour (43.53 kJ mol1 at 35 1C), R is the universal gas constant (kJ mol1 K1) and T is the temperature (K). After inserting Eqs. (4) and (5) into the GAB equation in Table 1, the nonlinear regression analysis was adopted to evaluate the parameters C0, K0, Xm, qm and qn. To evaluate the monolayer moisture contents (Xm), the BET (aw up to 0.4) and GAB (aw up to 0.9) models were used. Once the moisture content at the monolayer (Xm) was known, the sorption surface area of walnut kernels could be determined by the following equation (Gregg and Sing, 1982): S ¼ X m N A Am =M wat ¼ 35:3 X m ,

(6) 2

1

where S is the solid surface area (m g solids ), Xm the monolayer moisture content (% d.b.), Mwat is the molecular weight of water (18 kg kgmol1), NA the Avogadro’s number (6 1026 molecules kgmol1) and Am the area of a water molecule (1.06 1019 m2 molecule1). Menkov et al. (1999) have shown that the dependence between monolayer moisture content and temperature is well described by a linear equation. A modiﬁcation of the BET model yields X¼

ðAx þ Bx tÞCaw , ½ð1 aw Þð1 aw þ Caw Þ

X m ¼ Ax þ Bx t

(7) (8)

where t is the temperature (1C), X the EMC, aw the water activity and Ax, Bx and C are coefﬁcients independent of temperature. The coefﬁcients of Eq. (7) were determined using a nonlinear regression program on the experimental data at awp0.4. The (aw)x values corresponding to monolayer moisture content can be found by solving Eq. (7) after putting X ¼ Xm ¼ Ax+Bxt in Eq. (7). The (aw)x at which the monolayer forms is given by pﬃﬃﬃﬃ C1 . (9) ðaw Þx ¼ C1

2.2.2. Isosteric heat of sorption and sorption entropy Isosteric heat of sorption is the amount of energy required to change unit mass of a product from liquid to vapour at a particular temperature and water activity (Aviara et al., 2002). The net isosteric heat is the amount of energy by which the heat of vaporization of moisture in a product exceeds the latent heat of pure water (Labuza, 1968). Water sorption data from the best-ﬁtting equation for three temperatures were used to calculate the isosteric heat of sorption by the method of linearization of the Clausius–Clapeyron equation (Tsami et al., 1990). It is a measure of the interaction between an absorbate

and absorbent: dðln aw Þ st Qn ¼ R dð1=TÞ x

(10)

1 where Qst n is the net isosteric heat of sorption (kJ mol ), aw 1 1 the water activity, R the gas constant (8.314 J mol K ) and T the absolute temperature (K). Qst n was obtained from the plot of the natural logarithms of water activity from the best-ﬁtting equation vs. 1/T for a speciﬁc moisture content. This procedure was repeated for many EMCs to determine the effect of EMC on the net isosteric heat of sorption. Subsequent computation of aw values corresponding to a given moisture content was carried out using an Excel spreadsheet. Although it is assumed that the Qst n is invariant with temperature, the application of this method requires the measurement of sorption isotherms at more than two temperatures. Isosteric heat of sorption (Qst) was calculated from the relationship:

Qst ¼ Qst n þ qc ,

(11)

where qc is the latent heat of vaporization of pure water (43.53 kJ mol1) at 35 1C, the average temperature used in this study. Entropy change plays an important role in the energy analysis of food processing systems. The differential entropy (entropy of sorption) of adsorption and desorption of water at each moisture content was obtained by ﬁtting Eq. (12) to equilibrium data from the best-ﬁtting equation (Aguerre et al., 1986): In aw ¼ Qst =ðRTÞ ðDS=RÞ.

(12)

DS can be calculated from Eq. (12) by plotting ln aw vs. 1/T for certain values of the moisture content and then determining the intercept (DS/R). This procedure was repeated for many values of moisture content in order to detect the dependence of sorption entropy on the moisture content. 2.2.3. Spreading pressure Spreading pressure (f), which is the surface excess free energy, was calculated using an analytical procedure described by Iglesias et al. (1976) Z K B T aw y f¼ daw . (13) Am 0 aw where the moisture ratio y is: y ¼ X =X m

(14) 23

1

where K is the Boltzmann’s constant (1.38 10 JK ), T the temperature (K) and Am the area of a water molecule (1.06 1019 m2). The value of spreading pressure was noted to be intermediate at aw ¼ 0. Calculation of the integral in Eq. (13) changes from a numerical procedure to assume an empirical relationship between water activity and moisture content. Therefore, in the present study the Dent model

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(Dent, 1977) was used: 10

(15)

Eq. (16) was used to determine the values of spreading pressure at different temperatures for adsorption and desorption. 2.2.4. Net integral enthalpy and entropy The net integral enthalpy (Qin), a measure of the food–water afﬁnity, was determined by a technique similar to that for the isosteric heat but at constant spreading pressure. Spreading pressure is regarded as the free surface energy of adsorption (Fasina et al., 1999): Qin dðln aw Þ ¼ (17) . R dðT1 Þ F

A plot of ln aw vs. 1/T at constant spreading pressure yielded the net integral enthalpy from the slope of the straight line obtained. Net integral entropy describes the degree of disorder and randomness of motion of water molecules. It quantiﬁes the mobility of the adsorbed water molecules, and indicates the degree to which the water–substrate interaction exceeds that of the water molecules (Mazza and LeMaguer, 1978). Net integral entropy (DSin) was determined by using the integral enthalpy from Eq. (18) (Mazza and LeMaguer, 1978) and the values obtained were plotted against moisture content: DS in ¼ Qin =T R In ðaw Þn ,

(18)

where (aw)* is the geometric mean water activity obtained at constant spreading pressure at different temperatures. 3. Results and discussion 3.1. Adsorption and desorption isotherms The change of the EMC with the equilibrium relative humidity (ERH) is given in Figs. 2 and 3. The nearly sigmoid shapes of the adsorption isotherm curves and the sigmoid shapes of the desorption isotherm curves at

8 EMC (% d.b.)

where b and b0 are the constants from the Dent sorption isotherm related to the properties of the adsorbed water (dimensionless). The parameters b and b0 in Eq. (15) were determined by nonlinear regression analysis by using the monolayer moisture content obtained by applying the BET equation in Table 1 to the experimental data on equilibrium moisture relationships. Substituting Eq. (15) into Eq. (13), rearranging and then integrating gives the spreading pressure on the basis of surface area per sorption site or area per one molecule of water on each sorption site as K BT 1 þ b0 aw baw f¼ ln . (16) Am 1 baw

6

4

2

0 0

20

40

60

80

100

ERH (%) Fig. 2. Moisture adsorption isotherms of walnut kernels at selected temperatures (m, experimental 25 1C; J, experimental 35 1C; K, experimental 45 1C; ___, predicted 25 1C; – -–, predicted 35 1C; - - -, predicted 45 1C).

12

10

8 EMC (% d.b.)

aw 1 b0 2b bðb0 bÞ 2 ¼ þ aw a , b0 X m b0 X m b0 X m w X

6

4

2

0 0

20

40

60

80

100

ERH (%) Fig. 3. Desorption isotherm data of walnut kernels at three temperatures (m, experimental 25 1C; J, experimental 35 1C; K, experimental 45 1C; ___, predicted 25 1C; – - –, predicted 35 1C; - - -, predicted 45 1C).

different temperatures can be observed from Figs. 2 and 3. In the ﬁrst segment (with low r.h.) of the S-shaped sorption isotherm curves, walnut kernels sorbed relatively lower amounts of moisture. However, larger amount of moisture was absorbed at higher r.h. Similar behaviour has been reported by other authors for different foods (Sanni et al., 1997; McLaughlin and Magee, 1998). According to Van den Berg and Bruin (1981), a general sigmoid sorption isotherm can be divided into three different parts; ranges I

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(aw ¼ 0–0.22), II (aw ¼ 0.22–0.73) and III (aw ¼ 0.73–1.0). In ranges II and III, water molecules penetrate newly created pores of the already swollen structure and are mechanically entrapped in the void spaces. Therefore, water uptake particularly at higher water activity would be markedly inﬂuenced by the stability of the microporous structure. The data also indicated that the EMC decreased with increasing temperature, at a constant equilibrium r.h., thus indicating that walnut kernels became 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 and LeMaguer, 1980). But, there was no marked difference in the EMCs with increasing temperature. The analysis of variance (ANOVA) showed that the effect on temperature on moisture content was insigniﬁcant (P40.05). The effect of temperature on the sorption isotherm is of great importance given that foods are exposed to a 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 (Al-Muhtaseb et al., 2004a). Fig. 4 shows the sorption isotherms at 25 1C. Hysteresis between adsorption and desorption was shown over almost the entire range of water activity at 25 1C. Similar behaviour of adsorption and desorption isotherms was observed for 35 and 45 1C. The ANOVA showed that adsorption and desorption data was insigniﬁcantly different (P40.05). Iglesias and Chirife (1976a) recognized that it is not possible to give a single explanation of the hysteresis phenomena in foods due to food being a complex 12

10

EMC (% d.b.)

8

6

combination of various constituents which cannot only sorb water independently but also interact among themselves. Similar hysteresis phenomena have been reported for some foods (Palou et al., 1997; Johnson and Brennan, 2000; Al-Muhtaseb et al., 2004a). No microbial deterioration was observed during experiments. 3.2. Evaluation of fitting ability of sorption models The best ﬁtted coefﬁcients of the equations and r2, E (%), average residual, and RMSE are listed in Table 2. The applicability of the BET equation is generally restricted to aw values below 0.45 because of the assumptions used in the derivation of the equation (Labuza, 1968). The lower is the values of E %, average residual and RMSE, the better will be the goodness of ﬁt. Examination of the results in Table 2 indicated that the Peleg model best describes the experimental adsorption and desorption data for walnut kernels throughout the entire range of water activity. The Peleg model gives E (%) values ranging from 2.57–2.96% with average values of 2.61% for adsorption and from 5.39 to 7.24% with average values of 6.25% for desorption. In the range of water activity 0.4–0.9 aw, the Smith model could be considered to best represent experimental data since it reached E % values lower than 10%. It gave average r2, E %, RMSE values of 0.9931, 2.34 and 0.171 for adsorption and 0.9900, 2.65 and 0.162 for desorption, respectively. The Oswin and Caurie models were inadequate for representing the sorption isotherms of walnut kernels, giving average E values of 17.22% and 11.01% for adsorption, and 14.51% and 14.69% for desorption, respectively. The comparison between the best ﬁt (Peleg model) and the experimental values is shown in Figs. 2 and 3. Fig. 5 shows the correlation between the values predicted by the Peleg model and the experimental values of the EMC of walnut kernels for adsorption (r2 ¼ 0.9991). Similar plots were obtained for desorption (r2 ¼ 0.9917, graph not shown). This agreement was further analyzed in Fig. 6, showing the standardized residuals versus the predicted values of EMC. The standardized residual is deﬁned as R ¼ ðei eave Þ=RMSE,

4

2

0 0

20

40

60 ERH (%)

80

100

Fig. 4. Adsorption and desorption isotherms of walnut kernels at 25 1C showing the hysteresis effect (K, experimental (adsorption); J, experimental (desorption); ___, predicted (adsorption); - - -, predicted (desorption)).

(19)

where ei is the difference between the experimental and the predicted viscosities, and eave is the mean of the residuals. Since there was a random distribution and the error variance appeared constant, the Peleg model is usable for the evaluation of water sorption behaviour of walnut kernels. For Henderson, Iglesias and Chirife, Oswin, Smith models, the residuals plots displayed a systematic pattern. A typical graph was that for the Henderson model (Fig. 7). Weisser (1986) proposed using the exponential relationships between GAB parameters (Xm, C and K) and temperature to extend the GAB model to incorporate the temperature effect. From the estimated values of parameters in Table 2, no exponential temperature function

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Table 2 The best-ﬁtted coefﬁcients for isotherm equations Model

Constants

Adsorption 25 1C

Desorption 35 1C

45 1C

25 1C

35 1C

45 1C

GAB

Xm C K r2 E eave RMSE

3.729 3.135 0.752 0.9992 2.141 0.0024 0.0830

3.761 2.833 0.742 0.9992 2.379 0.0007 0.0841

14.31 0.651 0.508 0.9965 7.703 0.0383 0.1730

14.36 3.340 0.261 0.9645 9.600 0.0411 0.5603

4.285 8.405 0.658 0.9857 8.383 0.0080 0.3427

4.468 6.787 0.645 0.9858 9.427 0.0119 0.3441

BET

Xm C r2 E eave RMSE

3.088 2.512 0.9980 3.535 0.0057 0.0500

2.852 2.670 0.9987 3.031 0.0043 0.0388

2.902 2.101 0.9970 4.443 0.0069 0.0536

4.180 3.963 0.9999 0.533 0.0005 0.0126

4.271 3.685 0.9992 1.510 0.0003 0.0493

4.595 2.731 0.9961 3.736 0.0011 0.1083

Henderson

A B r2 E eave RMSE

0.123 1.267 0.9990 3.438 0.0096 0.0962

0.132 1.256 0.9983 3.389 0.0100 0.1195

0.155 1.190 0.9965 4.365 0.0133 0.1717

0.037 1.781 0.9854 8.482 0.0070 0.3598

0.034 1.842 0.9858 9.2689 0.0124 0.3412

0.040 1.770 0.9851 11.05 0.0192 0.3523

Iglesias and Chirife

a b r2 E eave RMSE

0.911 2.328 0.9946 4.906 0.0412 0.1720

0.863 2.339 0.9958 4.130 0.0370 0.1388

0.756 2.441 0.9972 3.181 0.0249 0.1300

1.415 1.807 0.9437 11.78 0.1234 0.55345

1.422 1.762 0.9399 11.66 0.1239 0.5410

1.370 1.815 0.9447 13.75 0.1106 0.5407

Oswin

A B r2 E eave RMSE

3.817 0.462 0.9836 16.80 0.0550 0.3874

3.652 0.464 0.9814 16.55 0.0550 0.3978

3.442 0.485 0.9889 18.32 0.0605 0.4317

4.986 0.349 0.9779 12.36 0.0293 0.4367

4.918 0.337 0.9739 13.88 0.0320 0.4629

4.7812 0.349 0.9693 17.28 0.0390 0.5057

Peleg

m1 n1 m2 n2 r2 E eave RMSE

7.820 1.013 5.809 6.191 0.9995 2.572 0.0011 0.0709

6.825 0.956 5.712 4.780 0.9993 2.287 0.00001 0.0773

5.843 0.938 6.367 3.983 0.9986 2.958 0.00042 0.1099

8.791 0.718 12.07 15.26 0.9943 5.385 0.0104 0.2254

9.466 14.76 8.690 0.718 0.9931 6.122 0.0113 0.2380

9.999 16.30 8.854 0.776 0.9924 7.235 0.0137 0.2522

Smith

c1 c2 r2 E eave RMSE

0.617 4.325 0.9867 8.797 0.0617 0.2890

0.570 4.169 0.9933 8.461 0.0570 0.2850

0.410 4.156 0.9867 7.161 0.0410 0.2719

1.684 4.108 0.96024 13.90 0.1684 0.6373

1.721 3.932 0.9221 15.47 0.1721 0.6664

1.581 3.969 0.9145 18.09 0.1581 0.6796

Caurie

a b r2 E eave RMSE

0.021 2.600 0.9821 11.24 0.0301 0.2606

0.076 2.619 0.9835 10.77 0.0266 0.2337

0.203 2.747 0.9862 11.02 0.0158 0.2244

0.564 1.977 0.9269 13.21 0.1110 0.5816

0.575 1.925 0.9214 14.03 0.1098 0.5747

0.518 1.984 0.9251 16.84 0.0940 0.5846

Up to a 0.4. w

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260

10

Xpi ( % d.b.)

8 6 4 2 0 0

2

4

6 Xei (% d.b.)

8

10

Fig. 5. Plot of experimental and predicted equilibrium moisture content for adsorption.

Standardized residual

4.0

2.0

0.0

-2.0

-4.0 0

3

6 Xei (% d.b.)

9

12

Fig. 6. Plot of residuals ﬁt of the Peleg model to sorption data of walnut kernels (K, adsorption; J, desorption).

Standardized residual

4.0

2.0

0.0

rption. C0, K0, Xm, DHc (qm–qn) and DHk (qc–qn), evaluated with Eqs. (4) and (5) being substituted into the GAB equation, were found to be 1.66, 0.097, 12.6 (d.b.), 1.55 kJ mol1 and 4.15 kJ mol1 for adsorption (r2 ¼ 0.9904) and 1.59, 0.875, 4.23 (d.b.), 4.17 kJ mol1 and 0.476 kJ mol1 for desorption (r2 ¼ 0.9814), respectively. DHc represents the difference in enthalpy between monolayer and multi-layer sorption (Van den Berg, 1984). The negative DHc value for adsorption has also been reported by Myhara et al. (1998) for Khalas dates. The DHc value for desorption is higher than the value for adsorption. DHk represents the difference between the heat of condensation of water and the heat of sorption of the multi-layer (Van den Berg, 1984). The positive DHk values indicate endothermic interaction of water with the material. The BET equation is based on adsorption onto a free surface without capillary condensation and therefore is applicable to adsorption for the mono and multi-layer regions of the isotherm. A monolayer moisture content in the BET isotherm equation that ﬁts the obtained data is regarded as the sorption capacity of the adsorbent and as the indicator of usefulness of polar sites for water vapour (Chung and Pfost, 1967). The speciﬁc surface area plays an important role in determining the water binding properties of particulate materials. The values of surface area from Eq. (6) by using the monolayer moisture values obtained from the BET equation (aw ¼ 0–0.40) were 109.01, 100.68, and 102.44 m2g solids1 for adsorption and 147.55, 150.77, and 162.20 m2g solids1 for desorption, for the equilibrium temperatures of 25, 35, and 45 1C, respectively. The coefﬁcients of Eq. (7) were Ax ¼ 3.673, Bx ¼ 0.0212, and C ¼ 2.442 for adsorption (r2 ¼ 0.9965) and Ax ¼ 3.944, Bx ¼ 0.0108, and C ¼ 3.438 for desorption (r2 ¼ 0.9961). The calculated values of (aw)x from Eq. (9) for adsorption and desorption were 0.3902 and 0.3504, respectively. The moisture level considered to be safest with reference to good storage stability of foods is the monolayer value. Since the coefﬁcient C in Eq. (9) is independent of temperature, the walnut kernels stored at (aw)x should have a moisture content equal to the monolayer moisture content for extending the shelf life with minimal deterioration. 3.3. Isosteric heat of sorption and sorption entropy

-2.0

-4.0 0

3

6 Xei (% d.b.)

9

12

Fig. 7. Plot of residuals ﬁt of the Henderson model to sorption data of walnut kernels (K, adsorption; J, desorption).

could be found for the parameters of Xm, C and K. A more detailed analysis of the GAB parameters can provide further valuable information about adsorption and deso-

The energy requirements of heat and mass transfer in biological systems can be studied for the thermodynamic approach (Rizvi and Benado, 1984). The isosteric heats of adsorption and desorption determined by applying Eqs. (10) and (11) to sorption EMC data as expressed by the moisture sorption isotherm model that best described EMC and water activity relationships were represented as a function of moisture in Fig. 8. Isosteric heats of adsorption increased to a maximum and then decreased with the increase in moisture content. The maximum isosteric heats of adsorption were obtained

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15 Entropy of sorption (J mol-1K-1)

55

Isosteric heat (kJ mol-1)

261

52

49 46

43

40

12 9 6 3 0 -3

0

2

4 6 Moisture content (% d.b.)

8

10

0

2

4 6 Moisture content (% d.b.)

8

10

Fig. 8. Variation of isosteric heat of adsorption and desorption with moisture content (K, adsorption; J, desorption).

Fig. 9. Sorption entropy versus moisture content (K, adsorption; desorption).

in the moisture content range 1.5–2.5% dry basis and were between 50.4 and 49.9 kJ mol1. The maximum enthalpy value indicates the covering of the strongest binding sites and the greatest water–solid interaction. The covering of less favourable locations and the formation of multi-layers then follow, as shown by the decrease in enthalpy with increasing moisture content. Isosteric heats of desorption decreased with the increase in moisture content and the trend seemed to become asymptotic as a moisture content of 7% dry basis was approached. This conﬁrms the fact that at higher moisture levels, the strength of water binding decreases. Different polar groups on the water binding polymers in foods and changes in the dimensions and geometry of the polymers during sorption are thought to give rise to this range of activity in sorption sites (McLaughlin and Magee, 1998). At low moisture levels, the adsorption is mainly at the monomolecular layer where the sorption sites are usually active (Iglesias and Chirife, 1976b). Similar trends have been reported for the isosteric heats of some foods (Palou, et al., 1997; Aviara et al., 2002; Ajibola et al., 2003; McMinn and Magee, 2003). The heat of desorption ranged from 52 kJ mol1 at 1% (d.b.) moisture content to 44.2 kJ mol1 at 9.5% (d.b.) moisture content. The isosteric heat of adsorption was calculated for moisture content ranging from 1–9% (d.b.). Correspondingly, the heat of adsorption ranged from 48.7–44.4 kJ mol1. The isosteric heats of adsorption and desorption were higher than the latent heat of vaporization of pure water, indicating that the energy of binding between the water molecules and the sorption sites was higher than the energy which holds the water molecules together in the liquid phase. Fig. 8 revealed that the heat required for the adsorption process was generally greater than that for the desorption process. As the moisture content increased, the differences in isosteric heat values for adsorption and desorption processes were observed to decrease. The difference between the heats of adsorption

and desorption was greater at lower moisture contents, converging as moisture content increased and practically disappearing above 5% moisture content (d.b.). These changes are probably due to changes in molecular structure during sorption which affects the degree of activation of sorption sites. No relationship exists between the degree of hysteresis and the variation in the isosteric heats of sorption (Al-Muhtaseb et al., 2004b). Substituting Eqs. (4) and (5) into the GAB equation, at the water activity (aw)x corresponding to the monolayer moisture content (12.6% d.b., for adsorption; 4.23% d.b., for desorption), the isosteric heats of adsorption and desorption were calculated as 46.1 and 49.8 kJ mol1, respectively. The isosteric heat of desorption was close to the qm value (47.22 kJ mol1) estimated by Eqs. (4) and (5), thereby implying a good ﬁt of this model to the experimental data. However, the isosteric heat of adsorption was not close to the qm value (37.83 kJ mol1) estimated by Eqs. (4) and (5), thereby indicating a poor ﬁt of the GAB model to the experimental data. Also, although E deviation values for adsorption were less than 10% and so superﬁcially supported a good ﬁt for the GAB model, this was caused by a negative value for the enthalpy difference (DHc) between mono- and multi-layer sorption. Fig. 9 shows the sorption entropy for walnut kernels as a function of moisture content Adsorption entropy of walnut kernels was low at low moisture content, but it then increased rapidly with increase in moisture content in the moisture range of 1–2.5% d.b. Above a moisture content of 2.5% dry basis, the adsorption entropy of walnut kernels decreased sharply with increase in moisture content Thereafter, it remained nearly constant until a moisture content of 9% (d.b.) was attained. Desorption entropy decreased smoothly with increasing moisture content to a minimum value at about 6.5% (d.b.) moisture content (Fig. 9). It then increased smoothly with moisture content.

J,

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Spreading pressure (Jm2)

Adsorption

Desorption

aw

25 1C

35 1C

45 1C

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.0127 0.0239 0.0341 0.0439 0.0536 0.0634 0.0737 0.0850 0.0980

0.0140 0.0261 0.0371 0.0476 0.0579 0.0683 0.0793 0.0914 0.1053

0.0114 0.0219 0.0318 0.0416 0.0513 0.0614 0.0722 0.0841 0.0980

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.0189 0.0332 0.0451 0.0558 0.0657 0.0752 0.0846 0.0941 0.1042

0.0188 0.0332 0.0452 0.0559 0.0658 0.0753 0.0847 0.0941 0.1040

0.0168 0.0302 0.0417 0.0520 0.0616 0.0708 0.0799 0.0890 0.0984

3.4. Net integral enthalpy and entropy The constants b and b0 in Eq. (15) at 25, 35 and 45 1C were found to be 0.8004, 0.8112, 0.8084 and 3.571, 3.841, 2.921, respectively, for adsorption (r2 ¼ 0.9981, 0.9968, 0.9961), and 0.6847, 0.6596, 0.6307 and 5.827, 5.580, 4.693, respectively, for desorption (r2 ¼ 0.9845, 0.9857, 0.9854). The spreading pressures of walnut kernels are presented in Table 3. The results show that the spreading pressure increased with increasing water activity at any temperature. The net integral enthalpy of adsorption slightly increased with increasing moisture content, and then maintained a constant level (Fig. 10). The net integral enthalpy values of desorption were closely similar at all moisture contents. The net integral enthalpy values for adsorption were greater than those for desorption at any moisture content value. Fasina et al. (1997, 1999) and Aviara and Ajibola (2002) respectively identiﬁed a similar response for the net integral enthalpy of alfalfa pellet, gari and cassava. In Fig. 11, the net integral entropy of adsorption and desorption of walnut kernels is plotted as a function of moisture content. The net integral entropy of adsorption decreased gradually with increasing moisture content to a minimum value at about 6.1% (d.b.) moisture content, and then slightly increased in magnitude with further increases in moisture content. The minimum net integral entropy of adsorption 327.9 kJ mol1 was observed at a moisture content of 6.1% (d.b.) of walnut kernels. No marked difference was observed between the desorption entropies. The initial decrease in the net integral entropy shows the loss of rotational freedom or degree of randomness of the water molecules as the readily available sites become

120 Net integral enthalpy (kJ mol-1)

Table 3 Spreading pressures of walnut kernels at different water activities and temperatures

100

80 60

40

20 0

2

4 6 Moisture content (% d.b.)

8

Fig. 10. Net integral enthalpy of sorption versus moisture content (K, adsorption; J, desorption).

-110 Net integral entropy (J mol-1K-1)

262

-160 -210 -260 -310 -360 0

2

4 6 Moisture content (% d.b.)

8

10

Fig. 11. Effect of moisture content on the net integral entropy of walnut kernels (K, adsorption; J, desorption).

saturated and the strongest binding sites are used. The subsequent increase in magnitude reﬂects the occurrence of more freely held water molecules and the formation of multi-layers. The newly-bound water molecules held less strongly possess more freedom as a result of a gradual opening and swelling of the material (Bettelheim et al., 1970). The integral entropy of adsorption differed considerably from the integral entropy of desorption in magnitude. In all cases the net integral entropy of sorbed water was negative in magnitude. Iglesias et al. (1976) explained that this behaviour might be attributed to the existence of chemical adsorption and or structural modiﬁcations of the adsorbent. The highly negative value of the net integral entropy at low moisture content conﬁrms the notion that an initial small percentage of water is very tightly bound (Rizvi, 1986). Similar trends have been reported on the adsorption entropy of moisture sorption in sugar beet root (Iglesias et al., 1976), winged bean seed (Fasina et al., 1999), cassava (Aviara and Ajibola, 2002), sesame seed (Aviara et al., 2002) and soya bean (Aviara et al., 2004).

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4. Conclusions The sorption isotherms obtained in this investigation had a sigmoid shape. The EMCs were found to decrease with increasing temperature at constant water activity. They were also found to increase with increasing water activity at constant temperature. Hysteresis is evident over the entire range of water activity. Peleg’s (1993) model was found to be the most appropriate equation for representing the walnut kernels sorption isotherms. The isosteric heat of desorption decreased with increase in moisture content. The isosteric heats of sorption attained the free water point at a moisture content of 7% (d.b.). Adsorption entropy of walnut kernels increased rapidly with increase in moisture content to 2.5% (d.b.), and then decreased sharply with further increase in moisture content. Desorption entropy decreased smoothly with increasing moisture content to 6.5% (d.b.). It then increased smoothly with moisture content. Spreading pressure increased with increasing water activity. Net integral enthalpy of adsorption increased with moisture content to a maximum value and then showed no further change with moisture content. Net integral entropy of adsorption decreased with moisture content to a minimum value at 6.1% (d.b.) and then increased, reﬂecting transition from occupation of easily accessible sites to increased localized binding, followed by formation of mobile multi-layers. Moisture content did not affect the net integral enthalpy nor the net integral entropy of desorption. Acknowledgement This study was supported by Scientiﬁc Research Department of Fırat University (Project no. FU¨BAP-793). References Aguerre, R.J., Suarez, C., Viollaz, P.E., 1986. Enthalpy–entropy compensation in sorption phenomena: application to the prediction of the effect of temperature on food isotherms. Journal of Food Science 51, 1547–1549. Aguerre, R.J., Suarez, C., Viollaz, P.E., 1989. New BET type multilayer sorption isotherms: Part II. Modelling water sorption in foods. Lebensmittel-Wissenschaft und-Technologie 22, 192–195. Ajibola, O.O., Aviara, N.A., Ajetumobi, O.E., 2003. Sorption equilibrium and thermodynamic properties of cowpea (Vigna unguiculata). Journal of Food Engineering 58, 317–324. Al-Muhtaseb, A.H., McMinn, W.A.M., Magee, T.R.A., 2004a. Water sorption isotherms of starch powders. Part 1: Mathematical description of experimental data. Journal of Food Engineering 61, 297–307. Al-Muhtaseb, A.H., McMinn, W.A.M., Magee, T.R.A., 2004b. Water sorption isotherms of starch powders. Part 2: Thermodynamic characteristics. Journal of Food Engineering 62, 135–142. Aviara, N.A., Ajibola, O.O., 2002. Thermodynamics of moisture sorption in melon seed and cassava. Journal of Food Engineering 55, 107–113. Aviara, N.A., Ajibola, O.O., Dairo, U.O., 2002. Thermodynamics of moisture sorption in sesame seed. Biosystems Engineering 83, 423–431. Aviara, N.A., Ajibola, O.O., Oni, S.A., 2004. Sorption equilibrium and thermodynamic characteristics of soya bean. Biosystems Engineering 87, 179–190.

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