- Email: [email protected]
Dielectric properties of α-d -glucose aqueous solutions at 2450 MHz
Food Research International 36 (2003) 485–490 www.elsevier.com/locate/foodres
Dielectric properties of a-d-glucose aqueous solutions at 2450 MHz Xiangjun Liaoa, G.S.V. Raghavana,*, Jianming Daia, V.A. Yaylayanb a
Department of Agricultural AND Biosystems Engineering, Macdonald Campus of McGill University, 21,111 Lakeshore Road, Ste-Anne-de-Bellevue, Quebec, Montreal, Canada H9X3V9 b Deptartment of Food Science and Agricultural Chemistry, Macdonald Campus of McGill University, 21,111 Lakeshore Road, Ste-Anne-de-Bellevue, Quebec, Montreal, Canada H9X3V9 Received 28 September 2001; accepted 2 November 2002
Abstract Using a cavity perturbation technique, dielectric properties of a-d-glucose aqueous solution at 2450 MHz were measured at concentrations ranging from 10 to 60% in the temperature range of 0–70 C. Dielectric constant increases with temperature in a quadratic manner while linearly decreasing with glucose concentration. Dielectric loss factor decreases with temperature in a quadratic way. The loss factor–concentration relationship depends on the temperature. At lower temperature, loss factor increases linearly with concentration up to a certain concentration then decreases. At temperatures higher than 40 C, loss factor linearly increases with concentration at all concentration ranges studied. The results are useful for studying volumetric heating of these solutions by microwave energy, and chemical changes such as Maillard reaction and mutarotation involving glucose aqueous solutions in microwave field. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Dielectric properties; Dielectric constant; Loss factor; 2450 MHz; Glucose solution
1. Introduction The successful use of microwave is directly associated with the dielectric properties of the material. Dielectric properties are key factors in the better understanding of the interactions of microwaves with food materials. Dielectric properties of materials are defined in terms of dielectric constant (e0 ) and loss factor (e00 ). e0 Is a measure of the ability of a material to couple with microwave energy and e00 is a measure of the ability of a material to heat by absorbing microwave energy (Mudgett, 1986). Although many foods can be heated by microwave energy, less satisfactory products are obtained in the microwave oven. This is attributed to the short heating time insufficient to complete the reactions involving the formation of food color and flavor. In order to improve the quality of a product in a microwave field, it is necessary to use a suitable for* Corresponding author. Fax: +1-514-398-8387. E-mail address: [email protected] (G.S.V. Raghavan).
mulation that can enhance the desired reactions to produce the desirable color and flavor. Dielectric properties of materials, to some degree, will give an idea which formulation will be heated in a microwave field since microwave heating is directly linked to dielectric properties of materials. The Maillard reaction is a typical chemical reaction in food processing and flavor chemistry. It has far reaching implications in the production of flavors and aromas, nutrition, toxicology, human pathology, and technology of food processing (Ikan, 1996; Yaylayan, 1997). Glucose is an important reducing sugar participating in the Maillard reaction. Its water solution has peculiar optical activity (Volodymyr, 1996). Many investigations on the dielectric properties of glucose aqueous solutions exist, but none of them have focused on microwave frequency of 2450 MHz and different temperatures. Roebuck, Goldblith, and Westohal (1972) reported the dielectric properties of glucose aqueous solutions at 25 C at microwave frequencies of 3000 and 1000 MHz. Some studies on dielectric relaxation of glucose solutions to explain and determine the motion or structure of molecules in the solutions have
0963-9969/03/-see front matter # 2002 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0963-9969(02)00196-5
486
X. Liao et al. / Food Research International 36 (2003) 485–490
been reported (Chan, Pathmanathan, & Johari, 1986; Mashimo, Nobuhiro, & Toshihiro, 1992; Moran, Jeffrey, Thomas, & Stevens, 2000; Noel, Parker, & Ring, 1996; Suggett, 1976). In addition, dielectric properties of glucose solutions were considered to elucidate the behavior and molecular dynamics by others (Fuchs & Kaatze, 2001; Hochtl, Boresch, & Steinhauser, 2000). However, these dielectric properties do not contribute to the study of underlying mechanisms of microwaveassisted chemical reactions involving glucose solutions. The misconception that solvents possessing higher dielectric constants heat rapidly while those with lower dielectric constants heat slowly under microwave has misled many people in their selection of heating media for chemical reactions or extractions in a microwave field. When a material absorbs microwaves at 2450 or 915 MHz, the temperature profile for the material is dependent on both the dielectric constant and loss factor at these frequencies, not just on dielectric constants as mentioned in the literature. As different types of glucose solutions differentially affect the heating characteristics of material during microwave heating, the selection of solutions is the most influential factor on the heating rate of microwave-assisted chemical reactions. However, data on dielectric properties of a-dGlucose aqueous solutions (10–60%) at 2450 MHz and elevated temperatures are rare or non-existent. Furthermore, there are no reports about the relationships (models) between the dielectric properties of a-d-glucose aqueous solutions, the temperature and their concentrations. The dielectric behavior of glucose solutions of different concentrations when exposed to microwaves at different temperatures would be useful in the understanding of microwave-assisted Maillard reactions involving glucose (Liao, Raghavan, & Yaylayan, 2000). It also aids in the understanding of the mechanism of mutarotation and microwave-enhanced chemical reac-
tions. Based on the facts mentioned, it prompted us to investigate the dielectric properties of a-d-glucose aqueous solution at 2450 MHz at varying temperatures.
2. Materials and methods 2.1. Materials a-d-Glucose was purchased from Aldrich Chemical Company, Inc. (USA) and was used without further purification. 2.2. Glucose aqueous solutions The solutions were prepared by adding amounts of glucose into suitable bottles, which were filled up with distilled water to the specific volumes. Microwave heating was employed to make them dissolve completely. In order to avoid any effects from disintegration of glucose by microorganisms and precipitation, the measurement started as soon as the temperature of sample was cooled to 0 C. 2.3. Dielectric properties measurements Dielectric properties at 2450 MHz were measured using the cavity perturbation technique, requiring a dielectric analyzer (Meda & Raghavan, 1998), a PC, a resonant cavity made of copper (i.d.=90 mm; h=45 mm; TM010 simplistic mode), and heating/cooling unit (Isotemp 1013S, Fisher Scientific Inc.; Fig. 1). The system was calibrated with distilled water, a liquid of known dielectric properties. The sample was confined in a 10-ml borosilicate glass sample holder (Fisherbrand Micropipets). The circulating fluid, ethylene glycol, transferred heat from coils attached to the external walls of the resonant cavity, thus maintaining the temperature
Fig. 1. Schematic diagram of measurement set-up.
X. Liao et al. / Food Research International 36 (2003) 485–490
of the cavity and sample at desired level. Dielectric measurements of all glucose solutions were performed at specific temperatures discussed. The accuracy for temperature measurement was 0.1 C. The following equations were used to calculate e0 and e00 . Vo "0 ¼ 1 þ 0:539 ðfÞ ð1Þ Vs Vo 1 1 00 " ¼ 0:269 ð2Þ Qs Qo Vf f ¼
fo fs fs
ð3Þ
487
where: Vs and Vo are the volumes of the sample and the cavity, respectively; fo and fs are the resonant frequencies of the empty and sample loaded cavity, respectively; Qo and Qs are the quality factors of the empty and sample loaded cavity, respectively.
3. Results and discussion Dielectric properties are critical parameters in processes involving microwave heating. For a mixture, both dielectric constant and loss factor are functions of temperature as well as the composition of the mixture
Fig. 2. Influence of temperature on the dielectric constant of glucose solutions at different concentrations (^): 10%; (&): 20%; (~): 30%; ( ) 40%; (&): 45%; (*): 50%; (+): 56%; (): 60%.
Fig. 3. Influence of concentration on the dielectric constant of glucose solution at different temperatures (^): 0 C; (&): 10 C; (~): 20 C; ( ) 30 C; (&): 40 C; (*): 50 C; (+): 60 C; (): 70 C.
488
X. Liao et al. / Food Research International 36 (2003) 485–490
(Favreau, Sosle, & Raghavan, 1997; Tulasidas, Raghavan, van de Voort, & Girard, 1995).
"0 ¼ AT 2 þ BT þ C ¼ ð1 xÞðAw T 2 þ Bw T þ Cw Þ þ xðAg T 2 þ Bg T þ Cg Þ ¼ Ag Aw x þ Aw T 2 þ Bg Bw x þ Bw T ð8Þ þ Cg Cw x þ Cw
3.1. Effect of concentration and temperature on the dielectric constant of glucose solutions For a given concentration, the dielectric constant increases with temperature as shown in Fig. 2. As temperature increases, the difference in the dielectric constant for different concentrations decreases. This observation may be due to the fact that the net increase in the number of free molecules with temperature for higher concentration is larger than that for the lower concentration. Quadratic regression can be applied to the dielectric constant–temperature relationship at each concentration (see Fig. 2). This observation agrees with Tulasidas et al. (1995) for sugar solutions and grape juice and with Faveau et al. (1997) for maple sap on the quadratic dielectric constant–temperature relationship. For a given temperature, the dielectric constants generally decrease with the increase of glucose concentration as shown in Fig. 3. This observation is similar to the report on carbohydrates (Roebuck et al., 1972). Variation of e0 with the increase of concentration at given temperatures are linear and significant (a=0.0001) with a coefficient of variation (CV) between 2 and 5% (see Fig. 3). The slope of the regression line increases with temperature suggesting that the dielectric constant at lower temperature is more influenced by concentration than that at higher temperature. The linearity of the e0 –concentration relationship indicates that as far as the dielectric constant is concerned there is no interaction between the two components. The dielectric constant as it appears in twocomponent system is directly contributed from each individual component and can be written as: "0 ¼ ð1 xÞ"0w þ x"0g
ð4Þ
where e0 is the dielectric constant of the mixture, x is concentration of glucose solution (wt./wt.), "0 w is the contribution of dielectric constant from water, and "0 g is the contribution from glucose. At given concentrations, "0 ¼ AT 2 þ BT þ C
ð5Þ
where: A, B, C are constants and T is temperature in C. Assuming that contributions of dielectric constant from water and glucose are in quadratic correlation with temperature: "0w ¼ Aw T 2 þ Bw T þ Cw
ð6Þ
"0g ¼ Ag T 2 þ Bg T þ Cg
ð7Þ
where Aw, Bw, Cw, Ag, Bg, and Cg are constants. Eq. (4) can than be written as:
constants Aw, Bw, Cw, Ag, Bg, and Cg can be obtained by the linear regression of the quadratic regression constants from Fig. 2 at a concentration range of 10–50%. Contributions from each individual component can then be expressed as quadratic equations: "0w ¼ 0:0017T 2 þ 0:2853T þ 87:224 "0g
2
¼ 0:0122T þ 2:0354T 21:37
ð9Þ ð10Þ
The dielectric constant for the glucose solution with concentration from 10 to 50% can be expressed as a function of temperature and concentration: "0 ¼ ð0:0139x þ 0:0017ÞT 2 þ ð1:7501x þ 0:2853ÞT þ ð108:594x þ 87:224Þ
ð11Þ
It is in linear and quadratic correlation with concentration and temperature, respectively. 3.2. Effect of concentration and temperature on the loss factor of glucose solutions For a given concentration, the loss factor generally decreases with the increase of temperature as shown in Fig. 4. Similar to the dielectric constant, a quadratic regression can be used to analyze the loss factor– temperature relationship at different concentrations. This observation is in agreement with Favreau et al. (1997) on the quadratic loss factor–temperature relationship. The influence of concentration on loss factor at different temperature is shown in Fig. 5. Different from that for the dielectric constant, the loss factor–temperature relationship varies with temperature. At lower temperature, the loss factor linearly increases with concentration up to a certain concentration value then decreases. However, when temperature is above 40 C, the loss factor linearly increases with concentration at the whole concentration range studied. This can be explained by the degree of saturation of glucose in water. The solubility of glucose in water varies greatly with temperature. For example, at the 25 C, the solubility is 91 g/100 ml water, however this value increase to 357 g/100 ml at 70 C. In the case of this study, at lower temperature, glucose solution becomes saturated at lower concentration. Before the solution reaching
X. Liao et al. / Food Research International 36 (2003) 485–490
489
Fig. 4. Influence of temperature on the dielectric loss factor of glucose solutions at different concentrations (^): 10%; (&): 20%; (~): 30%; ( ) 40%; (&): 45%; (*): 50%; (+): 56%; (): 60%.
saturate concentration, dielectric loss factor increases linearly with the increase of concentration. After reaching saturate concentration, the loss factor starts decreasing. With the increase of temperature, the saturation concentration increases dramatically; therefore the linearity keeps to a higher concentration as shown in Fig. 5. When the temperature is above 40 C, solutions are not saturated at all the concentration
range studied, resulting in the linearity through out the studied range of concentration. Similar to that of dielectric constant, the linearity between loss factor and concentration for unsaturated glucose solution suggests that loss factor of this two component system are contributed directly from each individual components. No interaction exists between water and glucose molecules in term of their contribu-
Fig. 5. Influence of concentration on the dielectric loss factor of glucose solution at different temperatures (^): 0 C; (&): 10 C; (~): 20 C; ( ) 30 C; (&): 40 C; (*): 50 C; (+): 60 C; (): 70 C.
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X. Liao et al. / Food Research International 36 (2003) 485–490
tion to loss factor. However for super-saturated glucose solution, the interaction between water and glucose molecules causes the decrease in loss factor.
4. Conclusions Dielectric properties of a-d-glucose aqueous solution were shown to be dependent on both temperature and concentration. The dielectric constant generally increases with the increase in temperature, while the loss factor decreases with the temperature. Both dielectric constant and loss factor have quadratic response to the temperature change. Glucose concentration affects the dielectric constant and loss factor differently. Dielectric constant linearly decreases with the increase of concentration at the whole concentration range studied. While for the loss factor, the concentration range can be divided into unsaturated and saturated solution. In the unsaturated range, dielectric loss factor linearly increase with the increase of concentration; however when it becomes super saturated solution, the loss factor decrease with the concentration. The linearity of both dielectric constant and loss factor at the unsaturated concentration suggests that the dielectric property as it appears is a direct summation of the values from both components. The off-linearity for the loss factor in the super-saturated concentration indicates an interaction between water and glucose molecules.
Acknowledgements We thank CIDA (Canadian International Development Agency) and NSERC (Natural Science Engineering Research Council of Canada) for their financial support to this research. Acknowledgement is also given to Dr. Venkatesh Sosle for his help in this paper.
References Chan, R. K., Pathmanathan, K., & Johari, G. P. (1986). Dielectric relaxations in the liquid and glassy states of glucose and its water mixtures. The Journal of Physical Chemistry, 90, 6358–6362.
Favreau, D., Sosle, V., & Raghavan, G. S. V. (1997). Dielectric properties of maple sap and syrup at 2.45 GHz. Journal of Microwave Power and Electromagnetic Energy, 32(2), 96–100. Fuchs, K., & Kaatze, U. (2001). Molecular dynamics of carbohydrate aqueous solutions: dielectric relaxation as a function of glucose and fructose concentration. The Journal of Physical Chemistry B, 105, 2036–2042. Hochtl, P., Boresch, S., & Steinhauser, O. (2000). Dielectric properties of glucose and maltose solutions. Journal of Chemical Physics, 112, 9810–9821. Ikan, R. (1996). The Maillard reaction: consequences for the chemical and life science. New York: John Wiley & Sons. Liao, X., Raghavan, G. S. V., & Yaylayan, V. A. (2000). Application of dielectric properties in microwave assisted Maillard reaction before reaching boiling. Microwave 2000: Sustainable Technology for the New Millenium and the third Chinese Microwave Chemistry Symposium.30 Tianjin, P.R. China. Mashimo, A., Nobuhiro, M., & Toshihiro, U. (1992). The structure of water determined by microwave dielectric study on water mixtures with glucose, polysaccharides, and L-ascorbic acid. Journal of Chemical Physics, 97, 6759–6765. Meda, S. V., & Raghavan, G. S. V. (1998). Dielectric properties measuring techniques—an overview of the development. NABEC (NorthEast Agricultural and Biological Engineering Conferences of the ASAE), Daltech, Halifax, Nova Scotia. Paper no. 9808. ASAE (American Society of Agricultural Engineerings), St. Joseph, MI, USA. Moran, G. R., Jeffrey, K. R., Thomas, J. M., & Stevens, J. R. (2000). A dielectric analysis of liquid and glassy solid glucose/water solutions. Carbohydrate Research, 328, 573–584. Mudgett, R. E. (1986). Microwave properties and heating characteristics of foods. Food Technology, 40, 84–93. Noel, T. R., Parker, R., & Ring, S. G. (1996). A comparative study of the dielectric relaxation behavior of glucose, maltose, and their mixtures with water in the liquid and glassy states. Carbohydrate Research, 282, 193–206. Roebuck, B. D., Goldblith, S. A., & Westohal, W. B. (1972). Dielectric properties of carbohydrate-water mixtures at microwave frequencies. Journal of Food Science, 37, 199–204. Suggett, A. (1976). Molecular motion and interactions in aqueous carbohydrate solutions III: a combined nuclear magnetic and dielectric-relaxation strategy. Journal of Solution Chemistry, 5, 33–46. Tulasidas, T. N., Raghavan, G. S. V., van de Voort, F., & Girard, R. (1995). Dielectric properties of grapes and sugar solutions at 2.45 GHz. Journal of Microwave Power and Electromagnetic Energy, 30(2), 117–123. Volodymyr, M. (1996). The peculiarities of glucose water solution optical activeness. International Conference of Conductive Breakdown Dielectric Liquids, Proceedings, 91–92. Yaylayan, V. A. (1997). Classification of the Maillard reaction: a conceptual approach. Trends in Food Science & Technology, 8, 13– 18.
Dielectric properties of a-d-glucose aqueous solutions at 2450 MHz Xiangjun Liaoa, G.S.V. Raghavana,*, Jianming Daia, V.A. Yaylayanb a
Department of Agricultural AND Biosystems Engineering, Macdonald Campus of McGill University, 21,111 Lakeshore Road, Ste-Anne-de-Bellevue, Quebec, Montreal, Canada H9X3V9 b Deptartment of Food Science and Agricultural Chemistry, Macdonald Campus of McGill University, 21,111 Lakeshore Road, Ste-Anne-de-Bellevue, Quebec, Montreal, Canada H9X3V9 Received 28 September 2001; accepted 2 November 2002
Abstract Using a cavity perturbation technique, dielectric properties of a-d-glucose aqueous solution at 2450 MHz were measured at concentrations ranging from 10 to 60% in the temperature range of 0–70 C. Dielectric constant increases with temperature in a quadratic manner while linearly decreasing with glucose concentration. Dielectric loss factor decreases with temperature in a quadratic way. The loss factor–concentration relationship depends on the temperature. At lower temperature, loss factor increases linearly with concentration up to a certain concentration then decreases. At temperatures higher than 40 C, loss factor linearly increases with concentration at all concentration ranges studied. The results are useful for studying volumetric heating of these solutions by microwave energy, and chemical changes such as Maillard reaction and mutarotation involving glucose aqueous solutions in microwave field. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Dielectric properties; Dielectric constant; Loss factor; 2450 MHz; Glucose solution
1. Introduction The successful use of microwave is directly associated with the dielectric properties of the material. Dielectric properties are key factors in the better understanding of the interactions of microwaves with food materials. Dielectric properties of materials are defined in terms of dielectric constant (e0 ) and loss factor (e00 ). e0 Is a measure of the ability of a material to couple with microwave energy and e00 is a measure of the ability of a material to heat by absorbing microwave energy (Mudgett, 1986). Although many foods can be heated by microwave energy, less satisfactory products are obtained in the microwave oven. This is attributed to the short heating time insufficient to complete the reactions involving the formation of food color and flavor. In order to improve the quality of a product in a microwave field, it is necessary to use a suitable for* Corresponding author. Fax: +1-514-398-8387. E-mail address: [email protected] (G.S.V. Raghavan).
mulation that can enhance the desired reactions to produce the desirable color and flavor. Dielectric properties of materials, to some degree, will give an idea which formulation will be heated in a microwave field since microwave heating is directly linked to dielectric properties of materials. The Maillard reaction is a typical chemical reaction in food processing and flavor chemistry. It has far reaching implications in the production of flavors and aromas, nutrition, toxicology, human pathology, and technology of food processing (Ikan, 1996; Yaylayan, 1997). Glucose is an important reducing sugar participating in the Maillard reaction. Its water solution has peculiar optical activity (Volodymyr, 1996). Many investigations on the dielectric properties of glucose aqueous solutions exist, but none of them have focused on microwave frequency of 2450 MHz and different temperatures. Roebuck, Goldblith, and Westohal (1972) reported the dielectric properties of glucose aqueous solutions at 25 C at microwave frequencies of 3000 and 1000 MHz. Some studies on dielectric relaxation of glucose solutions to explain and determine the motion or structure of molecules in the solutions have
0963-9969/03/-see front matter # 2002 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0963-9969(02)00196-5
486
X. Liao et al. / Food Research International 36 (2003) 485–490
been reported (Chan, Pathmanathan, & Johari, 1986; Mashimo, Nobuhiro, & Toshihiro, 1992; Moran, Jeffrey, Thomas, & Stevens, 2000; Noel, Parker, & Ring, 1996; Suggett, 1976). In addition, dielectric properties of glucose solutions were considered to elucidate the behavior and molecular dynamics by others (Fuchs & Kaatze, 2001; Hochtl, Boresch, & Steinhauser, 2000). However, these dielectric properties do not contribute to the study of underlying mechanisms of microwaveassisted chemical reactions involving glucose solutions. The misconception that solvents possessing higher dielectric constants heat rapidly while those with lower dielectric constants heat slowly under microwave has misled many people in their selection of heating media for chemical reactions or extractions in a microwave field. When a material absorbs microwaves at 2450 or 915 MHz, the temperature profile for the material is dependent on both the dielectric constant and loss factor at these frequencies, not just on dielectric constants as mentioned in the literature. As different types of glucose solutions differentially affect the heating characteristics of material during microwave heating, the selection of solutions is the most influential factor on the heating rate of microwave-assisted chemical reactions. However, data on dielectric properties of a-dGlucose aqueous solutions (10–60%) at 2450 MHz and elevated temperatures are rare or non-existent. Furthermore, there are no reports about the relationships (models) between the dielectric properties of a-d-glucose aqueous solutions, the temperature and their concentrations. The dielectric behavior of glucose solutions of different concentrations when exposed to microwaves at different temperatures would be useful in the understanding of microwave-assisted Maillard reactions involving glucose (Liao, Raghavan, & Yaylayan, 2000). It also aids in the understanding of the mechanism of mutarotation and microwave-enhanced chemical reac-
tions. Based on the facts mentioned, it prompted us to investigate the dielectric properties of a-d-glucose aqueous solution at 2450 MHz at varying temperatures.
2. Materials and methods 2.1. Materials a-d-Glucose was purchased from Aldrich Chemical Company, Inc. (USA) and was used without further purification. 2.2. Glucose aqueous solutions The solutions were prepared by adding amounts of glucose into suitable bottles, which were filled up with distilled water to the specific volumes. Microwave heating was employed to make them dissolve completely. In order to avoid any effects from disintegration of glucose by microorganisms and precipitation, the measurement started as soon as the temperature of sample was cooled to 0 C. 2.3. Dielectric properties measurements Dielectric properties at 2450 MHz were measured using the cavity perturbation technique, requiring a dielectric analyzer (Meda & Raghavan, 1998), a PC, a resonant cavity made of copper (i.d.=90 mm; h=45 mm; TM010 simplistic mode), and heating/cooling unit (Isotemp 1013S, Fisher Scientific Inc.; Fig. 1). The system was calibrated with distilled water, a liquid of known dielectric properties. The sample was confined in a 10-ml borosilicate glass sample holder (Fisherbrand Micropipets). The circulating fluid, ethylene glycol, transferred heat from coils attached to the external walls of the resonant cavity, thus maintaining the temperature
Fig. 1. Schematic diagram of measurement set-up.
X. Liao et al. / Food Research International 36 (2003) 485–490
of the cavity and sample at desired level. Dielectric measurements of all glucose solutions were performed at specific temperatures discussed. The accuracy for temperature measurement was 0.1 C. The following equations were used to calculate e0 and e00 . Vo "0 ¼ 1 þ 0:539 ðfÞ ð1Þ Vs Vo 1 1 00 " ¼ 0:269 ð2Þ Qs Qo Vf f ¼
fo fs fs
ð3Þ
487
where: Vs and Vo are the volumes of the sample and the cavity, respectively; fo and fs are the resonant frequencies of the empty and sample loaded cavity, respectively; Qo and Qs are the quality factors of the empty and sample loaded cavity, respectively.
3. Results and discussion Dielectric properties are critical parameters in processes involving microwave heating. For a mixture, both dielectric constant and loss factor are functions of temperature as well as the composition of the mixture
Fig. 2. Influence of temperature on the dielectric constant of glucose solutions at different concentrations (^): 10%; (&): 20%; (~): 30%; ( ) 40%; (&): 45%; (*): 50%; (+): 56%; (): 60%.
Fig. 3. Influence of concentration on the dielectric constant of glucose solution at different temperatures (^): 0 C; (&): 10 C; (~): 20 C; ( ) 30 C; (&): 40 C; (*): 50 C; (+): 60 C; (): 70 C.
488
X. Liao et al. / Food Research International 36 (2003) 485–490
(Favreau, Sosle, & Raghavan, 1997; Tulasidas, Raghavan, van de Voort, & Girard, 1995).
"0 ¼ AT 2 þ BT þ C ¼ ð1 xÞðAw T 2 þ Bw T þ Cw Þ þ xðAg T 2 þ Bg T þ Cg Þ ¼ Ag Aw x þ Aw T 2 þ Bg Bw x þ Bw T ð8Þ þ Cg Cw x þ Cw
3.1. Effect of concentration and temperature on the dielectric constant of glucose solutions For a given concentration, the dielectric constant increases with temperature as shown in Fig. 2. As temperature increases, the difference in the dielectric constant for different concentrations decreases. This observation may be due to the fact that the net increase in the number of free molecules with temperature for higher concentration is larger than that for the lower concentration. Quadratic regression can be applied to the dielectric constant–temperature relationship at each concentration (see Fig. 2). This observation agrees with Tulasidas et al. (1995) for sugar solutions and grape juice and with Faveau et al. (1997) for maple sap on the quadratic dielectric constant–temperature relationship. For a given temperature, the dielectric constants generally decrease with the increase of glucose concentration as shown in Fig. 3. This observation is similar to the report on carbohydrates (Roebuck et al., 1972). Variation of e0 with the increase of concentration at given temperatures are linear and significant (a=0.0001) with a coefficient of variation (CV) between 2 and 5% (see Fig. 3). The slope of the regression line increases with temperature suggesting that the dielectric constant at lower temperature is more influenced by concentration than that at higher temperature. The linearity of the e0 –concentration relationship indicates that as far as the dielectric constant is concerned there is no interaction between the two components. The dielectric constant as it appears in twocomponent system is directly contributed from each individual component and can be written as: "0 ¼ ð1 xÞ"0w þ x"0g
ð4Þ
where e0 is the dielectric constant of the mixture, x is concentration of glucose solution (wt./wt.), "0 w is the contribution of dielectric constant from water, and "0 g is the contribution from glucose. At given concentrations, "0 ¼ AT 2 þ BT þ C
ð5Þ
where: A, B, C are constants and T is temperature in C. Assuming that contributions of dielectric constant from water and glucose are in quadratic correlation with temperature: "0w ¼ Aw T 2 þ Bw T þ Cw
ð6Þ
"0g ¼ Ag T 2 þ Bg T þ Cg
ð7Þ
where Aw, Bw, Cw, Ag, Bg, and Cg are constants. Eq. (4) can than be written as:
constants Aw, Bw, Cw, Ag, Bg, and Cg can be obtained by the linear regression of the quadratic regression constants from Fig. 2 at a concentration range of 10–50%. Contributions from each individual component can then be expressed as quadratic equations: "0w ¼ 0:0017T 2 þ 0:2853T þ 87:224 "0g
2
¼ 0:0122T þ 2:0354T 21:37
ð9Þ ð10Þ
The dielectric constant for the glucose solution with concentration from 10 to 50% can be expressed as a function of temperature and concentration: "0 ¼ ð0:0139x þ 0:0017ÞT 2 þ ð1:7501x þ 0:2853ÞT þ ð108:594x þ 87:224Þ
ð11Þ
It is in linear and quadratic correlation with concentration and temperature, respectively. 3.2. Effect of concentration and temperature on the loss factor of glucose solutions For a given concentration, the loss factor generally decreases with the increase of temperature as shown in Fig. 4. Similar to the dielectric constant, a quadratic regression can be used to analyze the loss factor– temperature relationship at different concentrations. This observation is in agreement with Favreau et al. (1997) on the quadratic loss factor–temperature relationship. The influence of concentration on loss factor at different temperature is shown in Fig. 5. Different from that for the dielectric constant, the loss factor–temperature relationship varies with temperature. At lower temperature, the loss factor linearly increases with concentration up to a certain concentration value then decreases. However, when temperature is above 40 C, the loss factor linearly increases with concentration at the whole concentration range studied. This can be explained by the degree of saturation of glucose in water. The solubility of glucose in water varies greatly with temperature. For example, at the 25 C, the solubility is 91 g/100 ml water, however this value increase to 357 g/100 ml at 70 C. In the case of this study, at lower temperature, glucose solution becomes saturated at lower concentration. Before the solution reaching
X. Liao et al. / Food Research International 36 (2003) 485–490
489
Fig. 4. Influence of temperature on the dielectric loss factor of glucose solutions at different concentrations (^): 10%; (&): 20%; (~): 30%; ( ) 40%; (&): 45%; (*): 50%; (+): 56%; (): 60%.
saturate concentration, dielectric loss factor increases linearly with the increase of concentration. After reaching saturate concentration, the loss factor starts decreasing. With the increase of temperature, the saturation concentration increases dramatically; therefore the linearity keeps to a higher concentration as shown in Fig. 5. When the temperature is above 40 C, solutions are not saturated at all the concentration
range studied, resulting in the linearity through out the studied range of concentration. Similar to that of dielectric constant, the linearity between loss factor and concentration for unsaturated glucose solution suggests that loss factor of this two component system are contributed directly from each individual components. No interaction exists between water and glucose molecules in term of their contribu-
Fig. 5. Influence of concentration on the dielectric loss factor of glucose solution at different temperatures (^): 0 C; (&): 10 C; (~): 20 C; ( ) 30 C; (&): 40 C; (*): 50 C; (+): 60 C; (): 70 C.
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X. Liao et al. / Food Research International 36 (2003) 485–490
tion to loss factor. However for super-saturated glucose solution, the interaction between water and glucose molecules causes the decrease in loss factor.
4. Conclusions Dielectric properties of a-d-glucose aqueous solution were shown to be dependent on both temperature and concentration. The dielectric constant generally increases with the increase in temperature, while the loss factor decreases with the temperature. Both dielectric constant and loss factor have quadratic response to the temperature change. Glucose concentration affects the dielectric constant and loss factor differently. Dielectric constant linearly decreases with the increase of concentration at the whole concentration range studied. While for the loss factor, the concentration range can be divided into unsaturated and saturated solution. In the unsaturated range, dielectric loss factor linearly increase with the increase of concentration; however when it becomes super saturated solution, the loss factor decrease with the concentration. The linearity of both dielectric constant and loss factor at the unsaturated concentration suggests that the dielectric property as it appears is a direct summation of the values from both components. The off-linearity for the loss factor in the super-saturated concentration indicates an interaction between water and glucose molecules.
Acknowledgements We thank CIDA (Canadian International Development Agency) and NSERC (Natural Science Engineering Research Council of Canada) for their financial support to this research. Acknowledgement is also given to Dr. Venkatesh Sosle for his help in this paper.
References Chan, R. K., Pathmanathan, K., & Johari, G. P. (1986). Dielectric relaxations in the liquid and glassy states of glucose and its water mixtures. The Journal of Physical Chemistry, 90, 6358–6362.
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