- Email: [email protected]
Moisture adsorption of an Arabian sweet (basbusa) at different temperatures
Journal of Food Engineering 64 (2004) 187–192 www.elsevier.com/locate/jfoodeng
Moisture adsorption of an Arabian sweet (basbusa) at different temperatures Jasim Ahmed
a,*
, A.R. Khan b, A.S. Hanan
a
a
Department of Food Sciences, Faculty of Food Systems, United Arab Emirates University Al Ain, Post Box 17555, Al Ain, United Arab Emirates b Coastal and Air Pollution Division, Kuwait Institute of Scientific Research, Post Box 24885, 13109 Safat, Kuwait Received 30 May 2003; accepted 22 September 2003
Abstract Water sorption isotherm of basbusa, a traditional Arabian confectionary was studied over a selected temperature range (20–50 C). Various conventional models were tested to fit the experimental equilibrium moisture content data and it was found that the Dubinin–Astakhov model described adequately the moisture adsorption behavior of basbusa. The model included both temperature and water activity. Isosteric heat of sorption was found to be 3–119 kJ/mol for moisture contents range between 25 and 5%, respectively. 2003 Elsevier Ltd. All rights reserved. Keywords: Basbusa; Water sorption isotherm; Water activity; Isosteric heat; Differential enthalpy
1. Introduction Basbusa, a traditional Arabian confectionary is very popular in certain countries. The product preparation, storage and shelf-life vary significantly from country to country and ethnicity. No reliable information is available on production or market share of the product. The basic ingredients for the products are semolina (a byproduct of wheat flour during milling) (40%), sugar (20%), butter (20%) and yoghurt (20%) and a trace amount of baking powder. Sometimes people like to add coconut powder and dry nuts to increase the acceptability of the product. The ingredients are hand mixed thoroughly and the resulting dough is put in the oven for baking. A stock solution of sucrose is made in water (65–70Brix) and poured in the surface of the baked product several times to make a thin film of sugar. The product is sold without any packaging material as a result of which the product loses its crispiness. The sugar melts under the ambient temperatures of the Middle East countries going rise to the possible growth of undesirable microorganisms. Its moisture content is in the range of 15–25%, and it could be considered as an in-
*
Corresponding author. E-mail address: [email protected] (J. Ahmed).
0260-8774/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2003.09.031
termediate moisture food (IMF). The product is available in the traditional market; however, there is no mechanization of the product production so far. Besides, there is a lack of technical data on the product which could help to develop suitable packaging materials to enhance the marketability of the product. Relative humidity plays an important role in food product development, storage and packaging. A hygroscopic food product equilibrates with a humid environment after prolonged exposure at a constant temperature and reaches its equilibrium relative humidity. The equilibrium humidity between moist food and the surrounding is generally termed the water activity (aW ) while the relationship between water content and water activity at a given temperature is termed the moisture sorption isotherm (MSI). A critical aW (0.6– 0.7) exists below which no microorganism can grow (Beachut, 1981). It is well documented that water activity has significant a role in product safety and stability with respect to microbial growth, chemical/biochemical reaction rates, and physical properties (Fontana, 2000). The MSI of composite foods is one of the most important measures affecting acceptability, shelf-life and packaging and storage requirements. Water activity is a function of temperature. Temperature varies water activity due to changes in water binding, dissociation of water, solubility of solutes in
188
J. Ahmed et al. / Journal of Food Engineering 64 (2004) 187–192
Nomenclature aW water activity A adsorption potential (J mol1 ) A1 , B, C, K constants in Eqs. (1)–(6) n power in Eq. (3)–(6) N no. of observations P vapour pressure of water in food (Pa) P vapour pressure of pure water (Pa) R universal gas constant (J mol1 K1 ) T absolute temperature (K) xdb moisture contents dry basis (kg water/kg of dry matter)
water, or the state of the matrix. The effect of temperature on water activity of a food is product specific. Some cases the water activity increases with temperature while reverse trend is found in others (Khalloufi, Giasson, & Ratti, 2000; Myhara, Taylor, Slominski, & AlBulushi, 1998). Therefore, it is difficult to predict the direction of change of water activity with temperature. Adsorption phenomenon has been extensively used in separation processes and drying of foods. Various mathematical models for foods were developed either from theoretical or empirical concepts. The applicability of those models depends on equilibrium moisture content (EMC) and types of food stuffs. The BET isotherm, Eq. (1) (modified form of Langmuir isotherm) to incorporate multilayer adsorption was developed by Brunauer, Emmett, and Teller (1938). This model was further modified by Guggenheim (1966) based on the Anderson (1946) and de Boer (1953) theory and commonly known as the GAB isotherm (Eq. (2)) and is extensively used in moisture transfer in processed food. xdb CaW ¼ xM ð1 aW Þð1 ð1 CÞaW Þ xdb CKaW ¼ xM ð1 KaW Þð1 ð1 CÞKaW Þ
ð1Þ ð2Þ
Other types of correlations use logarithmic or power expressions for water activity, aW and are given as Henderson (1952) Eq. (3), Halsey (1948) Eq. (4), Oswin (1946) Eq. (5) and Chung and Pfost (1967) Eq. (6). These equations are empirical expressions to describe moisture adsorption behavior for different types of processed food. These equations have a temperature term and were used to reflect the temperature dependency of moisture adsorption. xdb ¼
lnð1 aW Þ A1 ðT þ BÞ
n
or aW ¼ 1 expðA1 ðT þ
1=n BÞxdb Þ
ð3Þ
monolayer moisture content, a constant of GAB equation negative of the thermal coefficient of the monolayer moisture contents differential molar enthalpy of adsorption (kJ mol1 ) differential molar entropy of adsorption (J mol1 K1 ) adsorption potential distribution (mol J1 )
xM a DH DS v
xdb ¼
expðA1 þ BT Þ ln aW
n
or 1=n
aW ¼ expðexpðA1 þ BT Þxdb Þ n aW xdb ¼ ðA1 þ BT Þ 1 aW
ð4Þ
or 1=n xdb A1 þ BT 1 ðT þ BÞ ln aW ¼ ln A1 C
1 ¼1þ aW xdb or aW ¼ exp
C expðA1 xdb Þ T þB
ð5Þ
ð6Þ
The most common adsorption expression (GAB equation) used for relating isotherm behavior, when applied to interpret temperature dependency, requires each constant to be described as an exponential function (Arrhenius type) of temperature, resulting into six parameters. There are some serious reservations about its application as reported by Chen (2003). In the present analysis the above listed equations are transformed into the standard form of adsorption expressions and have been used for moisture adsorption as a function of temperature for the common local confectionary (basbusa) in Middle Eastern countries. An exponential type of adsorption relation, the Dubinin–Astakhov equation (7) has been referred to extensively in the literature for heavy loading and recently Yu, Klein, and Reindl (2001) have used it for moisture adsorption on different adsorbents c xdb A ¼ exp ð7Þ B xM where A is adsorption potential equal to RT lnðP =P Þ or RT lnðaW Þ and B is characteristic energy equal to the
J. Ahmed et al. / Journal of Food Engineering 64 (2004) 187–192
adsorption potential at 36.8% of loading of the maximum capacity and is related to the size of micro-pores. The exponent c gives the curvature of the isotherm and is related to the heterogeneity of the micro-pores. Dubinin and Astakhov (1971) have proposed an extra temperature term including a thermal coefficient of limiting adsorption, a ! C xdb RT ln aW ¼ exp aðT T0 Þ ð8Þ xM B Basu, Henshaw, Biswas, and Kwan (2002) have compared adsorption isotherms with neural nets resulting in Eq. (8) for temperature dependence instead of the previous equation for isotherms only. The above equation can be rearranged to show that xM is an exponential function of T and same Eq. (7) can be used for temperature dependency. In the present study an attempt has been made to study the equilibrium moisture content (EMC) of basbusa to develop suitable packaging material.
189
3. Materials and methods Basbusa samples were purchased from a local departmental store in Al Ain city in the United Arab Emirates and used for the study. MSIs were estimated using the method described by Labuza (1984) at selected temperatures (20, 30, 40 and 50 C). The samples were cut vertically into smaller size but used Ôas prepared’ to get actual storage environment for the sorption experiments (Kim, Kim, Kim, Shin, & Chang, 1999). In this study we considered both desorption and adsorption isotherms. Samples of 12 mm · 12 · 12 mm were placed in a desiccators containing saturated salt solutions exhibiting the following aW values at 20 C: LiCl:0.113; MgCl2 :0.331; NaNO2 :0.654; NaCl:0.755; K2 SO4 :0.976 (Labuza, 1984). Samples in triplicate were considered for uniformity and calculation purpose. The equilibrium of the samples was considered when there was no weight difference higher than 0.1 mg/g between the previous weight and the current weight. The samples were equilibrated for between 19 and 21 days. Moisture content of the sample was measured by the oven drying method at 105 C for 6 h.
2. Parameter estimation P The objective function Nj¼1 ðxpredicted xexperiment Þ2j has db db been used to estimate the coefficients for the above correlations for the experimental data. This gave a very poor fit at low values of water activity. To solve this problem, the above objective function was modified to the sum of squares of percentage errors to provide an equal weight to each value throughout the experimental water activity range. The value of the mean absolute percentage error and correlation coefficient were selected as the test criterion for the goodness of fit for the correlation. The objective function is defined as sum of squares of the percentage errors, as objective function N h i2 X predicted experiment experiment ¼ xdb 100 xdb =xdb j
j¼1
ð9Þ
4. Results and discussion In Table 1, the comparison of the BET and GAB equations for adsorption isotherms is shown. It is observed that the GAB isotherm (Eq. (2)) fits the experimental data with minimum average absolute deviation for each temperature but fails to relate the temperature effects (no obvious trend for xM , C and K as a function of T ). The temperature dependent equations (3)–(6) are written in the standard form as Eqs. 1 and 2 in Table 2 by taking a constant as a common factor to represent xM for each equation. The coefficients of these correlations with the values of average % absolute error and correlation coefficients are listed for local confectionery in Table 2. Eqs. (3)–(6) represent the data within experimental accuracy of the moisture measurements. The average absolute percentage error is less than 5.5% and
Table 1 List of coefficients for BET and GAB isotherms for basbusa sweet Temperature (C)
Isotherm
xM
C
K
% deviation
r
20 30 40 50 20 30 40 50
BET BET BET BET GAB GAB GAB GAB
0.0412 0.0384 0.0328 0.0286 0.0786 0.0799 0.0594 0.0482
)3.172 )3.735 )3.506 )3.250 )25.43 17.44 )44.92 )19.10
– – – – 0.8094 0.7920 0.8333 0.8515
27.52 23.89 23.29 23.02 1.511 3.455 2.735 0.141
0.6272 0.7919 0.7903 0.7441 0.9982 0.9893 0.9926 0.9999
190
J. Ahmed et al. / Journal of Food Engineering 64 (2004) 187–192
Table 2 List of coefficients of equilibrium temperature dependent adsorption equations for basbusa sweet
(4) (5) (6) (7)
Correlations, xdb n WÞ xM lnð1a T þB n Þ xM expðBT ln aW n aW xM ð1 þ BT Þ 1a W xM ln ðT þBÞn ln aW n xM exp RT Bln aW
xM
n
1.4952
0.5723
6.7782
0.4353
0.5904
0.3579
0.0663 1004:3 T
0.023e
correlation coefficient ranges between 0.98 and 0.99. The values of xM evaluated for these equations are not consistent. These values show 100-fold variation and raise questions about the applicability of these empirical equations. Moisture adsorption in processed food is investigated in a narrow temperature range 20–50 C. Eqs. (3)–(6) include temperature effect but the GAB equation is also used for temperature dependency. Myhara et al. (1998) have reported that C and K (GAB equation constants) are exponential functions of temperature while xM is a constant for the most of the dried fruits. Khalloufi et al. (2000) have reported their experimental results about water activity of frozen dried mushrooms and berries. They concluded that berries do not show any temperature influence but mushrooms data can be well represented by GAB similar to the previous reference. Moreira, Vazquez, and Chenlo (2002) have reached the same conclusion for moisture adsorption of chickpeas. Lievonen and Roos (2002) have estimated six coefficients in the GAB equation for water adsorption of maltodextrin and poly(vinylpyrrolidone). The variations of adsorption data were not prominent within a narrow range of temperature. Stencl (1999) has studied water activity of skimmed milk powder and concluded that the Oswin equation (5) can represent the adsorption and desorption data adequately. Chen (2003) has concluded that GAB model is not applicable for moisture adsorption for pea seeds by comparing four temperature dependent models (Eqs. (3)–(6)) and found that Henderson equation (3) represents his and published data for pea seeds. An exponential expression, Eq. (7) with xM as a function of temperature incorporating Eq. (8), is used in this work to represent the experimental moisture adsorption data in the specified temperature range. The other thermodynamical properties, adsorption potential, enthalpy and entropy of adsorption as derived by Jaroniec, Madey, and Choma (1988) have also been evaluated. The Dubinin–Astakhov equation (7) has been extensively used in adsorption–desorption especially for energetically heterogeneous solids with micro- and
)159.41 0.3192
B
% Deviation
r
)250.47
6.78
0.9788
)0.0317
3.54
0.9890
)0.0026
4.12
0.9889
)269.06
5.87
0.9826
380.0
4.16
0.9887
macro-pores. Basbusa is porous and is complex in structure due to its ingredients and processing steps. Eq. (7) is an appropriate model to describe the moisture adsorption behavior. The optimum computed values of coefficients for the entire experimental temperature range of Eq. (7) and average absolute % error and correlation coefficient values are listed in Table 2. Fig. 1 compares the observed water activity data for basbusa at selected temperatures with the Dubinin–Astakhov equation. The comparison of various temperature dependent models for the experimental data at 30 C is shown as a residual plot in Fig. 2. It is obvious Eq. (7) represents the experimental data adequately and the computed values of the coefficients are more appropriate than other equations (Table 2). Isosteric heat of adsorption is also assessed at several water activity values using Clausius–Clapeypron equation. The moisture levels presented in Fig. 3 were chosen corresponding to the experimental equilibrium water activities. The slope of the semi-logarithmic regression lines with correlation coefficient, r values range between 0.987 and 0.988 and showed a decrease with the increase in moisture contacts, indicating a drop in binding energy for water molecules. These trends are reported for dates paste (Myhara et al., 1998) and maltodextrin and polyvinylpyrrolidone (Lievonen & Roos, 2002) showing
Temp. ( o C) 0.3
20 30
xdb (kg/kg)
Equations (3)
0.2
40 50 eqn 7
0.1
0 0
0.2
0.4 0.6 water activity aw
0.8
1
Fig. 1. Equilibrium sorption isotherms of basbusa at selected temperatures.
J. Ahmed et al. / Journal of Food Engineering 64 (2004) 187–192 12 8
+10% Equation No. 3
4
% deviation
191
4 0
5 6
-4
7 -8
-10%
-12 0.2
0.3
0.4
0.5 0.6 water activity aw
0.7
0.8
0.9
Fig. 2. Residual plot for Eqs. (3)–(6) of equilibrium moisture data of basbusa at 30 C.
aw
1
aw
1
0.1
moisture content x db (dry basis) 25%
20%
15%
10%
5%
0.1 3
3.1
3.2
3.3 1/T x 10 3 (K)
3.4
0.01 3.5
Fig. 3. Clausius and Clapeyron equation for different moisture contents of basbusa.
weaker interactions between complex sugar products and moisture. The thermodynamical function values of the adsorption potential distribution, vðAÞ the differential molar enthalpy, DHads and the differential molar entropy of adsorption, DSads are related to adsorption potential and given as: vðAÞ ¼
dðxdb =xM Þ dA
and aT ðxdb =xM Þ DH ¼ A vðAÞ and DS ¼
aðxdb =xM Þ vðAÞ
where a is the negative of the thermal coefficient of the M maximum adsorbed amount xM , i.e., a ¼ d lnx and is dT 1004:3 equal to T 2 for the present experimental results. The entropy and enthalpy values are negative to confirm the
necessity of sink to make this process possible. The enthalpy and entropy values show a decrease with increase in relative humidity or loading. The drop in isosteric heat is of large magnitude compared to differential enthalpy change.
5. Conclusion The moisture adsorption of Basbusa at different temperatures was experimentally investigated. Various temperature dependent published models have been tested for the experimental data. The exponential model, Eq. (7) represents the data with absolute mean deviation of less than 4% and correlation coefficient 0.986, thus validating the model. The isosteric heat of adsorption was calculated using the Clausius–Clapeypron equation and compared with the differential enthalpy and differential entropy of adsorption evaluated using the exponential model (Fig. 4).
192
J. Ahmed et al. / Journal of Food Engineering 64 (2004) 187–192 Adsorption potential 1000
10000 0
100 30 25
∆H and ∆S
-35 20 -70
15 ∆S (J mol-1 o K-1)
-105
10 5
-140
Isosetric heat (kJmol-1)
∆H (kJ
mol-1)
0 0
0.05
0.1
0.15 x db (kg/kg)
0.2
0.25
0.3
Fig. 4. Isosteric heat and differential enthalpy and entropy of adsorption of basbusa.
References Anderson, R. B. (1946). Modification of the BET equation. Journal of American Chemical Society, 68, 689–694. Basu, S., Henshaw, P. F., Biswas, N., & Kwan, H. K. (2002). Prediction of gas phase adsorption isotherms using neural nets. Canadian Journal of Chemical Engineering, 80, 1–7. Beachut, L. R. (1981). Microbial stability as affected by water activity. Cereal Foods World, 26(7), 345–349. Brunauer, S., Emmett, P. H., & Teller, E. (1938). Adsorption of gases in multi-molecular layers. Journal of American Chemical Society, 60, 309–316. Chen, C. (2003). Moisture sorption isotherms of pea seeds. Journal of Food Engineering, 58, 45–51. Chung, D. S., & Pfost, H. B. (1967). Adsorption and desorption of water vapour by cereal grains and their products. Transaction of the ASAE, 10, 549–554. de Boer, J. H. (1953). The dynamic character of adsorption. Oxford: Clarendon Press. Dubinin, M., & Astakhov, A. A. (1971). Description of adsorption equilibria of vapors on zeolites over wide range of temperature and pressure. In R. F. Gould (Ed.), Advances in Chemistry Series (102, pp. 69–85). Washington, DC: American Chemical Society.
Fontana, A. J. (2000). Understanding the importance of water activity in foods. Cereals Food World, 45(1), 7–10. Guggenheim, E. A. (1966). Application of Statistical Mechanics. Oxford: Clarendon Press. Halsey, G. (1948). Physical adsorption on non-uniform surfaces. Journal of Chemistry and Physics, 16, 931–945. Henderson, S. M. (1952). A basic concept of equilibrium moisture. Agricultural Engineering, 33, 29–32. Jaroniec, M., Madey, R., & Choma, J. (1988). Thermodynamic function associated with the exponential isotherm equation for gas adsorption on heterogeneous microporous solids. Journal of Colloid and Interface Science, 126, 69–73. Khalloufi, S., Giasson, J., & Ratti, C. (2000). Water activity of freeze dried mushrooms and berries. Canadian Agricultural Engineering, 42, 7.1–7.13. Kim, S. S., Kim, S. Y., Kim, D. W., Shin, S. G., & Chang, K. S. (1999). Moisture sorption characteristics of composite foods filled with chocolate. Journal of Food Science, 64, 300–302. Labuza, T.P., 1984. Moisture sorption: practical aspects of isotherm measurement and use. American Association of Cereal Chemists, St. Paul. MN. Lievonen, S. M., & Roos, Y. H. (2002). Water sorption of food models for studies of glass transition and reaction kinetics. Journal of Food Science, 67, 1758–1766. Moreira, R’., Vazquez, G., & Chenlo, F. (2002). Influence of the temperature on adsorption isotherms of chickpeas: evaluation of isosteric heat. Electronic Journal of Environmental Agricultural and Food Chemistry, 1, 1–11. Myhara, R. M., Taylor, M. S., Slominski, B. A., & Al-Bulushi, I. (1998). Moisture sorption isotherms and chemical composition of Omani dates. Journal of Food Engineering, 37, 471– 479. Oswin, C. R. (1946). The kinetics of package life III isotherm. Journal of Society of Chemical Industry, London, 65, 419– 421. Stencl, J. (1999). Water activity of skimmed milk powder in the temperature range of 20–45 C. Acta Veteriniria Brno, 68, 209– 215. Yu, D., Klein, S. A., & Reindl, D. T. (2001). An evaluation of silica gel for humidity control in display cases. Western Association for Art Conservation Newsletter, 23, 1–15.
Moisture adsorption of an Arabian sweet (basbusa) at different temperatures Jasim Ahmed
a,*
, A.R. Khan b, A.S. Hanan
a
a
Department of Food Sciences, Faculty of Food Systems, United Arab Emirates University Al Ain, Post Box 17555, Al Ain, United Arab Emirates b Coastal and Air Pollution Division, Kuwait Institute of Scientific Research, Post Box 24885, 13109 Safat, Kuwait Received 30 May 2003; accepted 22 September 2003
Abstract Water sorption isotherm of basbusa, a traditional Arabian confectionary was studied over a selected temperature range (20–50 C). Various conventional models were tested to fit the experimental equilibrium moisture content data and it was found that the Dubinin–Astakhov model described adequately the moisture adsorption behavior of basbusa. The model included both temperature and water activity. Isosteric heat of sorption was found to be 3–119 kJ/mol for moisture contents range between 25 and 5%, respectively. 2003 Elsevier Ltd. All rights reserved. Keywords: Basbusa; Water sorption isotherm; Water activity; Isosteric heat; Differential enthalpy
1. Introduction Basbusa, a traditional Arabian confectionary is very popular in certain countries. The product preparation, storage and shelf-life vary significantly from country to country and ethnicity. No reliable information is available on production or market share of the product. The basic ingredients for the products are semolina (a byproduct of wheat flour during milling) (40%), sugar (20%), butter (20%) and yoghurt (20%) and a trace amount of baking powder. Sometimes people like to add coconut powder and dry nuts to increase the acceptability of the product. The ingredients are hand mixed thoroughly and the resulting dough is put in the oven for baking. A stock solution of sucrose is made in water (65–70Brix) and poured in the surface of the baked product several times to make a thin film of sugar. The product is sold without any packaging material as a result of which the product loses its crispiness. The sugar melts under the ambient temperatures of the Middle East countries going rise to the possible growth of undesirable microorganisms. Its moisture content is in the range of 15–25%, and it could be considered as an in-
*
Corresponding author. E-mail address: [email protected] (J. Ahmed).
0260-8774/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2003.09.031
termediate moisture food (IMF). The product is available in the traditional market; however, there is no mechanization of the product production so far. Besides, there is a lack of technical data on the product which could help to develop suitable packaging materials to enhance the marketability of the product. Relative humidity plays an important role in food product development, storage and packaging. A hygroscopic food product equilibrates with a humid environment after prolonged exposure at a constant temperature and reaches its equilibrium relative humidity. The equilibrium humidity between moist food and the surrounding is generally termed the water activity (aW ) while the relationship between water content and water activity at a given temperature is termed the moisture sorption isotherm (MSI). A critical aW (0.6– 0.7) exists below which no microorganism can grow (Beachut, 1981). It is well documented that water activity has significant a role in product safety and stability with respect to microbial growth, chemical/biochemical reaction rates, and physical properties (Fontana, 2000). The MSI of composite foods is one of the most important measures affecting acceptability, shelf-life and packaging and storage requirements. Water activity is a function of temperature. Temperature varies water activity due to changes in water binding, dissociation of water, solubility of solutes in
188
J. Ahmed et al. / Journal of Food Engineering 64 (2004) 187–192
Nomenclature aW water activity A adsorption potential (J mol1 ) A1 , B, C, K constants in Eqs. (1)–(6) n power in Eq. (3)–(6) N no. of observations P vapour pressure of water in food (Pa) P vapour pressure of pure water (Pa) R universal gas constant (J mol1 K1 ) T absolute temperature (K) xdb moisture contents dry basis (kg water/kg of dry matter)
water, or the state of the matrix. The effect of temperature on water activity of a food is product specific. Some cases the water activity increases with temperature while reverse trend is found in others (Khalloufi, Giasson, & Ratti, 2000; Myhara, Taylor, Slominski, & AlBulushi, 1998). Therefore, it is difficult to predict the direction of change of water activity with temperature. Adsorption phenomenon has been extensively used in separation processes and drying of foods. Various mathematical models for foods were developed either from theoretical or empirical concepts. The applicability of those models depends on equilibrium moisture content (EMC) and types of food stuffs. The BET isotherm, Eq. (1) (modified form of Langmuir isotherm) to incorporate multilayer adsorption was developed by Brunauer, Emmett, and Teller (1938). This model was further modified by Guggenheim (1966) based on the Anderson (1946) and de Boer (1953) theory and commonly known as the GAB isotherm (Eq. (2)) and is extensively used in moisture transfer in processed food. xdb CaW ¼ xM ð1 aW Þð1 ð1 CÞaW Þ xdb CKaW ¼ xM ð1 KaW Þð1 ð1 CÞKaW Þ
ð1Þ ð2Þ
Other types of correlations use logarithmic or power expressions for water activity, aW and are given as Henderson (1952) Eq. (3), Halsey (1948) Eq. (4), Oswin (1946) Eq. (5) and Chung and Pfost (1967) Eq. (6). These equations are empirical expressions to describe moisture adsorption behavior for different types of processed food. These equations have a temperature term and were used to reflect the temperature dependency of moisture adsorption. xdb ¼
lnð1 aW Þ A1 ðT þ BÞ
n
or aW ¼ 1 expðA1 ðT þ
1=n BÞxdb Þ
ð3Þ
monolayer moisture content, a constant of GAB equation negative of the thermal coefficient of the monolayer moisture contents differential molar enthalpy of adsorption (kJ mol1 ) differential molar entropy of adsorption (J mol1 K1 ) adsorption potential distribution (mol J1 )
xM a DH DS v
xdb ¼
expðA1 þ BT Þ ln aW
n
or 1=n
aW ¼ expðexpðA1 þ BT Þxdb Þ n aW xdb ¼ ðA1 þ BT Þ 1 aW
ð4Þ
or 1=n xdb A1 þ BT 1 ðT þ BÞ ln aW ¼ ln A1 C
1 ¼1þ aW xdb or aW ¼ exp
C expðA1 xdb Þ T þB
ð5Þ
ð6Þ
The most common adsorption expression (GAB equation) used for relating isotherm behavior, when applied to interpret temperature dependency, requires each constant to be described as an exponential function (Arrhenius type) of temperature, resulting into six parameters. There are some serious reservations about its application as reported by Chen (2003). In the present analysis the above listed equations are transformed into the standard form of adsorption expressions and have been used for moisture adsorption as a function of temperature for the common local confectionary (basbusa) in Middle Eastern countries. An exponential type of adsorption relation, the Dubinin–Astakhov equation (7) has been referred to extensively in the literature for heavy loading and recently Yu, Klein, and Reindl (2001) have used it for moisture adsorption on different adsorbents c xdb A ¼ exp ð7Þ B xM where A is adsorption potential equal to RT lnðP =P Þ or RT lnðaW Þ and B is characteristic energy equal to the
J. Ahmed et al. / Journal of Food Engineering 64 (2004) 187–192
adsorption potential at 36.8% of loading of the maximum capacity and is related to the size of micro-pores. The exponent c gives the curvature of the isotherm and is related to the heterogeneity of the micro-pores. Dubinin and Astakhov (1971) have proposed an extra temperature term including a thermal coefficient of limiting adsorption, a ! C xdb RT ln aW ¼ exp aðT T0 Þ ð8Þ xM B Basu, Henshaw, Biswas, and Kwan (2002) have compared adsorption isotherms with neural nets resulting in Eq. (8) for temperature dependence instead of the previous equation for isotherms only. The above equation can be rearranged to show that xM is an exponential function of T and same Eq. (7) can be used for temperature dependency. In the present study an attempt has been made to study the equilibrium moisture content (EMC) of basbusa to develop suitable packaging material.
189
3. Materials and methods Basbusa samples were purchased from a local departmental store in Al Ain city in the United Arab Emirates and used for the study. MSIs were estimated using the method described by Labuza (1984) at selected temperatures (20, 30, 40 and 50 C). The samples were cut vertically into smaller size but used Ôas prepared’ to get actual storage environment for the sorption experiments (Kim, Kim, Kim, Shin, & Chang, 1999). In this study we considered both desorption and adsorption isotherms. Samples of 12 mm · 12 · 12 mm were placed in a desiccators containing saturated salt solutions exhibiting the following aW values at 20 C: LiCl:0.113; MgCl2 :0.331; NaNO2 :0.654; NaCl:0.755; K2 SO4 :0.976 (Labuza, 1984). Samples in triplicate were considered for uniformity and calculation purpose. The equilibrium of the samples was considered when there was no weight difference higher than 0.1 mg/g between the previous weight and the current weight. The samples were equilibrated for between 19 and 21 days. Moisture content of the sample was measured by the oven drying method at 105 C for 6 h.
2. Parameter estimation P The objective function Nj¼1 ðxpredicted xexperiment Þ2j has db db been used to estimate the coefficients for the above correlations for the experimental data. This gave a very poor fit at low values of water activity. To solve this problem, the above objective function was modified to the sum of squares of percentage errors to provide an equal weight to each value throughout the experimental water activity range. The value of the mean absolute percentage error and correlation coefficient were selected as the test criterion for the goodness of fit for the correlation. The objective function is defined as sum of squares of the percentage errors, as objective function N h i2 X predicted experiment experiment ¼ xdb 100 xdb =xdb j
j¼1
ð9Þ
4. Results and discussion In Table 1, the comparison of the BET and GAB equations for adsorption isotherms is shown. It is observed that the GAB isotherm (Eq. (2)) fits the experimental data with minimum average absolute deviation for each temperature but fails to relate the temperature effects (no obvious trend for xM , C and K as a function of T ). The temperature dependent equations (3)–(6) are written in the standard form as Eqs. 1 and 2 in Table 2 by taking a constant as a common factor to represent xM for each equation. The coefficients of these correlations with the values of average % absolute error and correlation coefficients are listed for local confectionery in Table 2. Eqs. (3)–(6) represent the data within experimental accuracy of the moisture measurements. The average absolute percentage error is less than 5.5% and
Table 1 List of coefficients for BET and GAB isotherms for basbusa sweet Temperature (C)
Isotherm
xM
C
K
% deviation
r
20 30 40 50 20 30 40 50
BET BET BET BET GAB GAB GAB GAB
0.0412 0.0384 0.0328 0.0286 0.0786 0.0799 0.0594 0.0482
)3.172 )3.735 )3.506 )3.250 )25.43 17.44 )44.92 )19.10
– – – – 0.8094 0.7920 0.8333 0.8515
27.52 23.89 23.29 23.02 1.511 3.455 2.735 0.141
0.6272 0.7919 0.7903 0.7441 0.9982 0.9893 0.9926 0.9999
190
J. Ahmed et al. / Journal of Food Engineering 64 (2004) 187–192
Table 2 List of coefficients of equilibrium temperature dependent adsorption equations for basbusa sweet
(4) (5) (6) (7)
Correlations, xdb n WÞ xM lnð1a T þB n Þ xM expðBT ln aW n aW xM ð1 þ BT Þ 1a W xM ln ðT þBÞn ln aW n xM exp RT Bln aW
xM
n
1.4952
0.5723
6.7782
0.4353
0.5904
0.3579
0.0663 1004:3 T
0.023e
correlation coefficient ranges between 0.98 and 0.99. The values of xM evaluated for these equations are not consistent. These values show 100-fold variation and raise questions about the applicability of these empirical equations. Moisture adsorption in processed food is investigated in a narrow temperature range 20–50 C. Eqs. (3)–(6) include temperature effect but the GAB equation is also used for temperature dependency. Myhara et al. (1998) have reported that C and K (GAB equation constants) are exponential functions of temperature while xM is a constant for the most of the dried fruits. Khalloufi et al. (2000) have reported their experimental results about water activity of frozen dried mushrooms and berries. They concluded that berries do not show any temperature influence but mushrooms data can be well represented by GAB similar to the previous reference. Moreira, Vazquez, and Chenlo (2002) have reached the same conclusion for moisture adsorption of chickpeas. Lievonen and Roos (2002) have estimated six coefficients in the GAB equation for water adsorption of maltodextrin and poly(vinylpyrrolidone). The variations of adsorption data were not prominent within a narrow range of temperature. Stencl (1999) has studied water activity of skimmed milk powder and concluded that the Oswin equation (5) can represent the adsorption and desorption data adequately. Chen (2003) has concluded that GAB model is not applicable for moisture adsorption for pea seeds by comparing four temperature dependent models (Eqs. (3)–(6)) and found that Henderson equation (3) represents his and published data for pea seeds. An exponential expression, Eq. (7) with xM as a function of temperature incorporating Eq. (8), is used in this work to represent the experimental moisture adsorption data in the specified temperature range. The other thermodynamical properties, adsorption potential, enthalpy and entropy of adsorption as derived by Jaroniec, Madey, and Choma (1988) have also been evaluated. The Dubinin–Astakhov equation (7) has been extensively used in adsorption–desorption especially for energetically heterogeneous solids with micro- and
)159.41 0.3192
B
% Deviation
r
)250.47
6.78
0.9788
)0.0317
3.54
0.9890
)0.0026
4.12
0.9889
)269.06
5.87
0.9826
380.0
4.16
0.9887
macro-pores. Basbusa is porous and is complex in structure due to its ingredients and processing steps. Eq. (7) is an appropriate model to describe the moisture adsorption behavior. The optimum computed values of coefficients for the entire experimental temperature range of Eq. (7) and average absolute % error and correlation coefficient values are listed in Table 2. Fig. 1 compares the observed water activity data for basbusa at selected temperatures with the Dubinin–Astakhov equation. The comparison of various temperature dependent models for the experimental data at 30 C is shown as a residual plot in Fig. 2. It is obvious Eq. (7) represents the experimental data adequately and the computed values of the coefficients are more appropriate than other equations (Table 2). Isosteric heat of adsorption is also assessed at several water activity values using Clausius–Clapeypron equation. The moisture levels presented in Fig. 3 were chosen corresponding to the experimental equilibrium water activities. The slope of the semi-logarithmic regression lines with correlation coefficient, r values range between 0.987 and 0.988 and showed a decrease with the increase in moisture contacts, indicating a drop in binding energy for water molecules. These trends are reported for dates paste (Myhara et al., 1998) and maltodextrin and polyvinylpyrrolidone (Lievonen & Roos, 2002) showing
Temp. ( o C) 0.3
20 30
xdb (kg/kg)
Equations (3)
0.2
40 50 eqn 7
0.1
0 0
0.2
0.4 0.6 water activity aw
0.8
1
Fig. 1. Equilibrium sorption isotherms of basbusa at selected temperatures.
J. Ahmed et al. / Journal of Food Engineering 64 (2004) 187–192 12 8
+10% Equation No. 3
4
% deviation
191
4 0
5 6
-4
7 -8
-10%
-12 0.2
0.3
0.4
0.5 0.6 water activity aw
0.7
0.8
0.9
Fig. 2. Residual plot for Eqs. (3)–(6) of equilibrium moisture data of basbusa at 30 C.
aw
1
aw
1
0.1
moisture content x db (dry basis) 25%
20%
15%
10%
5%
0.1 3
3.1
3.2
3.3 1/T x 10 3 (K)
3.4
0.01 3.5
Fig. 3. Clausius and Clapeyron equation for different moisture contents of basbusa.
weaker interactions between complex sugar products and moisture. The thermodynamical function values of the adsorption potential distribution, vðAÞ the differential molar enthalpy, DHads and the differential molar entropy of adsorption, DSads are related to adsorption potential and given as: vðAÞ ¼
dðxdb =xM Þ dA
and aT ðxdb =xM Þ DH ¼ A vðAÞ and DS ¼
aðxdb =xM Þ vðAÞ
where a is the negative of the thermal coefficient of the M maximum adsorbed amount xM , i.e., a ¼ d lnx and is dT 1004:3 equal to T 2 for the present experimental results. The entropy and enthalpy values are negative to confirm the
necessity of sink to make this process possible. The enthalpy and entropy values show a decrease with increase in relative humidity or loading. The drop in isosteric heat is of large magnitude compared to differential enthalpy change.
5. Conclusion The moisture adsorption of Basbusa at different temperatures was experimentally investigated. Various temperature dependent published models have been tested for the experimental data. The exponential model, Eq. (7) represents the data with absolute mean deviation of less than 4% and correlation coefficient 0.986, thus validating the model. The isosteric heat of adsorption was calculated using the Clausius–Clapeypron equation and compared with the differential enthalpy and differential entropy of adsorption evaluated using the exponential model (Fig. 4).
192
J. Ahmed et al. / Journal of Food Engineering 64 (2004) 187–192 Adsorption potential 1000
10000 0
100 30 25
∆H and ∆S
-35 20 -70
15 ∆S (J mol-1 o K-1)
-105
10 5
-140
Isosetric heat (kJmol-1)
∆H (kJ
mol-1)
0 0
0.05
0.1
0.15 x db (kg/kg)
0.2
0.25
0.3
Fig. 4. Isosteric heat and differential enthalpy and entropy of adsorption of basbusa.
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