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Moisture Sorption Isotherms of Vetch Seeds at Four Temperatures
J. agric. Engng Res. (2000) 76, 373}380 doi:10.1006/jaer.2000.0551, available online at http://www.idealibrary.com on
Moisture Sorption Isotherms of Vetch Seeds at Four Temperatures N. D. Menkov Department of Process Engineering, Higher Institute of Food Industry, 26, Maritza, Plovdiv 4000, Bulgaria; e-mail: nimenkov@hi$-plovdiv.acad.bg (Received 24 August 1999; accepted in revised form 1 March 2000)
The equilibrium moisture contents were determined for vetch seeds using the gravimetric static method at 5, 20, 40 and 603C over a range of relative humidities from 0)110 to 0)877. The sorption capacity of the seeds decreased with an increase in temperature at constant relative humidity. The hysteresis e!ect was lower at higher temperatures. Five equations were applied for analysing the experimental data: modi"ed Chung}Pfost, modi"ed Halsey, modi"ed Oswin, modi"ed Henderson, and Guggenheim}Anderson}de Boer (GAB) equations. The modi"ed Oswin model was the most suitable for describing the relationships between equilibrium moisture content, relative humidity and temperature. Vetch seeds maintained a monolayer moisture content when stored at a relative humidity in the range 0)17}0)18 regardless of the temperature. 2000 Silsoe Research Institute
Notation a, b, b , c, c , d D e G E K E Q h ,h H P H PK M M G M K G M K N P R t ¹
model coe$cients degree of freedom randomness of residual mean relative error, % standard error of moisture model coe$cients relative humidity, decimal relative humidity corresponding to monolayer moisture content, decimal moisture content, % d.b. measured value of the equilibrium moisture content, % d.b. predicted value of the equilibrium moisture content, % d.b. monolayer moisture content, % d.b. number of data points level of signi"cance universal gas constant, 8)314 kJ/kmol K temperature, 3C temperature, K
1. Introduction A number of models have been previously suggested to describe the relationship between equilibrium moisture 0021-8634/00/080373#08 $35.00/0
content (EMC) and equilibrium relative humidity (ERH) (Van den Berg & Bruin, 1981). Some of them take into account the e!ect of temperature. The modi"ed Chung} Pfost (Chung & Pfost, 1967; Pfost et al., 1976), modi"ed Henderson (Henderson, 1952; Thompson et al., 1968), modi"ed Halsey (Halsey, 1948; Iglesias & Chirife, 1976a), modi"ed Oswin (Oswin, 1946; Chen & Morey, 1989) & Guggenheim}Anderson}de Boer (GAB) (Van den Berg, 1984) equations have been adopted as standard equations by the American Society of Agricultural Engineers for describing sorption isotherms (ASAE, 1995). The monolayer moisture content is of signi"cant importance to the physical and chemical stability of dehydrated materials with regard to their lipid oxidation, enzyme activity, non-enzymatic browning, and structural characteristics (Labuza et al., 1970). It can be determined from the equilibrium sorption isotherms by means of the twoparameter Brunauer}Emmett}Teller (BET) equation (Brunauer et al., 1938). Vetch (
373
2000 Silsoe Research Institute
374
N. D . M EN K OV
of the legume seeds have a substantial in#uence on their germination and longevity (Roberts, 1972; Ellis et al., 1988,1990; Vertucci et al., 1994). Therefore, it is necessary to investigate the equilibrium moisture content relationships of vetch seeds for various relative humidities and temperatures to enable the storage conditions for the seeds to be correctly speci"ed. The automatic control of these conditions requires a reliable mathematical description of the EMC/ERH using suitable models. The object of this work was to obtain the equilibrium moisture isotherms for vetch seeds at 5, 20, 40 and 603C and to "t a suitable model for describing the sorption characteristics.
2.3. Analysis of data The description of the relationship between equilibrium moisture content, equilibrium relative humidity and temperature was veri"ed according to the following models: Modi"ed Chung}Pfost
!a H "exp exp (!cM) P t#b Modi"ed Halsey H "exp P
(1)
!exp (a#bt) MA
(2)
2. Material and methods
1 Modi"ed Oswin H " P (a#bt/M)A#1
2.1. Material
Modi"ed Henderson H "1!exp [!a(t#b)MA] P (4)
Vetch seeds of the 666 cultivar were provided in 1998 by the Institute for Plant Genetic Resources, Sadovo, Bulgaria. The seeds were harvested 6 months in advance, sun-dried to approximately 12% d.b. and kept at room temperature and at a relative humidity of less the 0)55.
2.2. Procedure The equilibrium moisture content of the vetch seeds was determined at 5, 20, 40 and 603C. The static gravimetric method was applied (Wolf et al., 1985). For the adsorption process, seeds were "rst dehydrated in a desiccator over P O at room temperature for 20 days to a moisture content below 1% d.b. Samples for desorption measurements were "rst hydrated in a glass jar over distilled water at 43C for 20 days to approximately 30% d.b. Samples of 4$0)2 g were weighed in weighing bottles. The weighing bottles were then placed in hygrostats with ten saturated salt solutions (LiCl, CH COOK, MgCl , K CO , NaBr, Mg(NO ) , SrCl , NaCl, KBr, KCl), used to obtain constant relative humidities environments (Greenspan, 1977; Weisser, 1986). All salts used were of reagent grade. At high relative humidities (ERH'0)70), crystalline thymol was placed in the hygrostats to prevent microbial spoilage of the seeds (Wolf et al., 1985). The hygrostats were kept in temperaturecontrolled cabinets at 5, 20, 40 and 60$0)23C. Samples were weighed with an accuracy of 0)0001 g every 3 days. Equilibrium was acknowledged when three consecutive weight measurements showed a di!erence of less than 0)001 g. The moisture content of each sample was determined by the vacuum oven method (AOAC, 1990). The equilibrium moisture contents were determined by calculating the means of triplicate measurements.
(3)
abcH P GAB M" (5) (1!bH ) (1!bH #bcH ) P P P where M is the moisture content in % d.b., H is the P relative humidity as a decimal, a, b and c are model coe$cients, and t is the temperature in 3C. The parameters b and c in the GAB equation can be correlated with temperature using the following Arrhenius-type equations (Labuza et al., 1985):
h b"b exp R¹
(6)
h c"c exp R¹
(7)
where b , c , h , and h are coe$cients, ¹ is the absolute temperature in K, and R is the universal gas constant in kJ/kmol K. A non-linear regression program was used to "t the "ve models to the experimental data. The suitability of the equations was evaluated and compared using the mean relative error E as a %, standard error of estimate K E and randomness of residual e (Chen & Morey, 1989): Q G 100 , M !M K G G E " (8) K N M G G , (M !M K ) G E" (9) G G Q d D e "M !M K (10) G G G where M is the measured EMC value, M K is the value G G predicted by the model, N is the number of data points, and d is the degrees of freedom of regression model D (number of data points minus number of constants in the model). Data points in a plot of the residual values versus
M O I ST U RE SO R PT IO N I S O TH ER M S
375
the predicted EMC values should tend to fall in horizontal band, centred zero, displaying no systematic tendencies toward a clear pattern. If the residual plots indicate a clear pattern, the model should not be accepted (Chen & Morey, 1989). The two-parameter BET equation is valid for ERH(0)45 (Labuza et al., 1985): M cH K P BET M" (11) (1!H )(1!H #cH ) P P P where M is the monolayer moisture content in % d.b. K The M values for each temperature were calculated K from BET equation, following an algorithm described previously (Iglesias & Chirife, 1976b). Menkov et al. (1999) established for a large number of biological products that the dependence between M and temperature K was well described by a linear equation. A modi"cation of the BET model yields (a#bt)cH P (12) Modi"ed BET M" (1!H ) (1!H #cH ) P P P M "a#bt (13) K The coe$cients of Eqn (12) were determined directly, using a non-linear, least-squares regression programme on the basis of experimental data at ERH(0)45. The values of monolayer moisture content were determined using Eqn (13). The ERH value H corresponding to the PK monolayer moisture content was determined by Eqn (12) after putting M"M (Iglesias & Chirife, 1976b): K (c!1 H " (14) PK c!1
Fig. 1. Adsorption and desorption isotherms of vetch seeds at 53C: , adsorption; , desorption; , modixed Oswin equation [Eqn (3)]
1999; Menkov, 2000). The EMC values of vetch seeds are similar to those obtained from other legume seeds * cowpea (Pappas & Rao, 1987), ¸athyrus pea (Mazza & Jayas, 1991). The values of coe$cients E and E for the four, K Q three-parameter models (modi"ed Chung}Pfost, modi"ed Halsey, modi"ed Oswin, and modi"ed Henderson), are presented in Table 3 for adsorption and in Table 4 for desorption. The parameters for the GAB models are presented in Table 5. Analysis of the residuals for adsorption is presented in Fig. 3, and for desorption in Fig. 4. For the modi"ed Chung}Pfost (adsorption and desorption) and modi"ed Halsey equations (desorption), the residual plots indicated a systematic pattern which made
3. Results and discussion Figures 1 and 2 give the experimental data obtained after adsorption and desorption performed on vetch seeds at 5 and 603C, respectively. The sorption isotherms have an S-shaped pro"le, typical of legume seeds (Vertucci & Leopold, 1987; Pappas & Rao, 1987; Mazza & Jayas, 1991; Menkov, 2000). The hysteresis e!ect was distinctly expressed at 53C. At 603C the di!erences in the adsorption and desorption data were not statistically signi"cant (level of signi"cance P)0)05) for most of the experimental points. The experimental data for adsorption and desorption are presented in Tables 1 and 2, respectively. The EMC values decreased with an increase in the temperature at constant ERH. Similar trends for many seeds have been reported in the literature (Vertucci & Leopold, 1987; Pappas & Rao, 1987; Mazza & Jayas, 1991; Suthar & Das, 1997; Walters & Hill, 1998; Menkov & Dinkov,
Fig. 2. Adsorption and desorption isotherms of vetch seeds at 603C: , adsorption; , desorption; , modixed Oswin equation [Eqn (3)]
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N. D . M EN K OV
Table 1 Equilibrium moisture content M in % d.b. obtained by adsorption at di4erent relative humidities Hr as a decimal and temperatures for vetch seeds 53C
203C
403C
603C
H, P dec.
M*, % d.b.
SDR
Hr , dec.
M, % d.b.
SD
Hr , dec.
M, % d.b.
SD
Hr , dec.
M, % d.b.
SD
0)113 0)245 0)336 0)431 0)589 0)635 0)757 0)771 0)851 0)877
5)2 7)7 9)2 10)6 13)0 14)0 17)7 19)2 23)1 24)8
0)06 0)22 0)17 0)08 0)19 0)14 0)14 0)18 0)14 0)25
0)113 0)231 0)331 0)432 0)544 0)591 0)725 0)755 0)817 0)851
4)8 7)6 8)8 10)3 10)9 11)9 14)5 16)9 21)2 22)6
0)10 0)11 0)19 0)21 0)13 0)07 0)13 0)17 0)21 0)29
0)112 0)201 0)316 0)432 0)484 0)532 0)658 0)747 0)794 0)823
4)1 5)5 7)7 8)4 8)7 9)8 12)8 15)6 16)7 18)8
0)08 0)13 0)18 0)24 0)09 0)05 0)18 0)07 0)11 0)16
0)110 0)160 0)293 0)432 0)440 0)497 0)580 0)745 0)789 0)803
3)6 4)6 5)8 7)3 7)5 8)3 9)5 12)9 14)1 14)5
0)05 0)10 0)08 0)24 0)17 0)25 0)17 0)13 0)13 0)12
* Mean of three replications. R Standard deviations based on three replications.
these equations unsuitable. The residuals obtained by all the other models denoted uniformly scattered points in residual plots. The modi"ed Oswin model had the lowest E and E values for adsorption and the lowest E value K Q K
for desorption compared to the other models. For description of the equilibrium isotherms of vetch seeds the modi"ed Oswin model is recommended. The GAB model is the second best model.
Table 2 Equilibrium moisture content M in % d.b. obtained by desorption at di4erent relative humidities Hr as a decimal and temperatures for vetch seeds 53C
203C
403C
603C
H, P dec.
M*, % d.b.
SDR
Hr , dec.
M, % d.b.
SD
Hr , dec.
M, % d.b.
SD
Hr , dec.
M, % d.b.
SD
0)113 0)245 0)336 0)431 0)589 0)635 0)757 0)771 0)851 0)877
6)5 9)8 10)8 12)2 15)5 17)1 19)0 21)2 23)3 29)2
0)09 0)07 0)18 0)16 0)08 0)22 0)21 0)11 0)16 0)25
0)113 0)231 0)331 0)432 0)544 0)591 0)725 0)755 0)817 0)851
5)5 8)0 9)8 11)1 12)1 13)0 17)2 21)7 23)0 24)5
0)14 0)20 0)13 0)12 0)10 0)21 0)29 0)06 0)21 0)21
0)112 0)201 0)316 0)432 0)484 0)532 0)658 0)747 0)794 0)823
4)5 6)4 7)8 9)8 10)0 10)5 13)5 16)9 17)4 20)2
0)16 0)13 0)21 0)02 0)12 0)17 0)13 0)12 0)19 0)16
0)110 0)160 0)293 0)432 0)440 0)497 0)580 0)745 0)789 0)803
3)7 4)7 6)0 7)8 7)8 8)5 10)0 14)1 15)4 17)0
0)06 0)18 0)20 0)07 0)06 0)24 0)20 0)04 0)23 0)11
* Mean of three replications. R Standard deviations on three replications. Table 3 Estimated values of coe7cients a, b, c; mean relative error Em, in % and standard error of moisture Es of three-parameter models for adsorption Estimated values
Parameter Modixed Chung}Pfost a b c E ,% K E Q
418)9 68)2 0)176 8)07 1)29
Modixed Halsey 4)302 !0)010 1)916 5)65 0)69
Modixed Oswin
Modixed Henderson
11)87 !0)057 2)48 3)79 0)58
0)00025 56)42 1)489 9)97 1)27
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M O I ST U RE SO R PT IO N I S O TH ER M S
Table 4 Estimated values of coe7cients a, b, c; mean relative error Em, in % and standard error of moisture Es of three-parameter models for desorption Estimated values
Parameter Modixed Chung}Pfost a b c E ,% K E Q
345)9 45)8 0)165 6)42 0)97
Modixed Halsey 4)498 !0)015 1)859 6)46 1)54
Modixed Oswin
Modixed Henderson
13)77 !0)083 2)65 4)32 0)85
0)00017 43)08 1)685 8)18 1)17
Fig. 3. Residual plots of xve models for the adsorption data of vetch seeds
378
N. D . M EN K OV
Table 5 Estimated values of coe7cients a, b0, c0, h1, h2; mean relative error Em, in % and standard error of moisture Es of the GAB model
Adsorption Desorption
a
b
c
h
h
Em , %
Es
6)68 8)16
0)413 0)360
0)0011 0)0009
1655)4 1825)7
24191 24114
5)23 5)49
0)68 0)74
The values of monolayer moisture content obtained by the standard procedure for adsorption and desorption at di!erent temperatures, are shown in Fig. 5. There is also a hysteresis e!ect with respect to the monolayer moisture content. The M values decreased with the increase in K
temperature. The values for the coe$cients a, b and c of Eqn (12) for adsorption are 6)85, !0)0397 and 21)19, respectively; and for desorption are 7)91, !0)042 and 24)12, respectively. Figure 5 shows a comparison of the monolayer moisture content values obtained by the
Fig. 4. Residual plots of xve models for the desorption data of vetch seeds
M O I ST U RE SO R PT IO N I S O TH ER M S
379
References
Fig. 5. Ewect of temperature on the monolayer moisture content for: (a) the Brunauer}Emmett}Teller (BET) model [Eqn (11)]; , adsorption; , desorption; and (b) the modixed BET model [Eqn (12)]; , adsorption; , desorption
standard procedure [Eqn (11)] and by direct procedure [Eqns (12) and (13)]. It can be noted that there is a close agreement between standard and direct procedures. The H value does not depend on temperature since the PK coe$cient c in Eqn (12) does not depend on the temperature. Despite the hysteresis e!ect, the values obtained for H are similar for adsorption and desorption (0)18 PK and 0)17, respectively).
4. Conclusions The equilibrium moisture content of vetch seeds (cultivar 666) have been determined by the static gravimetric method at four temperatures. The sorption capacity of vetch seeds decreased with an increase in temperature at constant relative humidity. The hysteresis e!ect was lower at higher temperatures. The experimental data were "tted to "ve models. The modi"ed Oswin model was the most suitable for describing the relationship between the equilibrium moisture content, the equilibrium relative humidity and temperature. Vetch seeds showed a monolayer moisture content when stored at relative humidity about in the range 0)17}0)18 regardless of the temperature.
Acknowledgements This study was conducted with the kind support of the National Research Fund * Bulgaria.
AOAC (1990). O$cial Methods of Analysis (15th Edn.). Association of O$cial Analytical Chemists, Washington, DC ASAE (1995). Standard D245.5. ASAE, St. Joseph, MI Aydogdu L; AcikgoK z E (1995). E!ect of seedling rate on seed and hay yield in common vetch (
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N. D . M EN K OV
Oswin C R (1946). The kinetics of package life. III. Isotherm. Journal of the Society of Chemical Industry, London, 65, 419}421 Pappas G; Rao V N M (1987). Sorption isotherms of cowpeas from 253C to 70 C. Transactions of the ASAE, 30, 1478}1483 Pfost H B; Mourer S G; Chung D S; Milliken G A (1976). Summarizing and reporting equilibrium moisture data for grains. ASAE Paper No. 76}3520, St. Joseph, MI Roberts E H (1972). Storage environment and the control of viability. In: Viability of Seeds (Roberts E H ed), pp 14}58. Chapman & Hall, London Suthar S H; Das S K (1997) Moisture sorption isotherms for karingda [Citrullus lanatus (Thumb) Mansf ] seed, kernel and hull. Journal of Food Process Engineering, 20, 349}366 Thompson T L; Peart R M; Foster G H (1968). Mathematical simulation of corn drying * a new model. Transactions of the ASAE, 11, 582}586 Van den Berg C (1984). Description of water activity of foods for engineering purposes by means of the GAB model of sorption. In: Engineering and Foods (McKenna B M ed), pp 119}131. Elsevier, New York
Van den Berg C; Bruin S (1981). Water activity and its estimation in food systems: theoretical aspects. In: Water Activity: In#uences on Food Quality (Rockland L B; Stewart G F eds), pp 1}61. Academic Press, London Vertucci C W; Roos E E; Crane J (1994). Theoretical basis of protocols for seed storage III. Optimum moisture contents for pea seeds stored at di!erent temperatures. Annals of Botany, 74, 531}540 Vertucci C W; Leopold A C (1987). Water binding in legume seeds. Plant Physiology, 85, 224}231 Walters C; Hill L M (1998). Water sorption isotherms of seeds from ultradry experiments. Seed Science Research, 8, 69}73 Weisser H (1986). In#uence of temperature on sorption isotherms. In: Food Engineering and Process Applications (Le Maguer M; Jelen P eds), Vol. 1, pp 189}200. Elsevier, New York Wolf W; Spiess W E L; Jung G (1985). Standardization of isotherm measurements (COST-project 90 and 90 bis). In: Properties of Water in Foods in Relation to Quality and Stability (Stimatos D; Multon J L eds), pp 661}679. Martinus Nijho! Publishers, Netherlands
Moisture Sorption Isotherms of Vetch Seeds at Four Temperatures N. D. Menkov Department of Process Engineering, Higher Institute of Food Industry, 26, Maritza, Plovdiv 4000, Bulgaria; e-mail: nimenkov@hi$-plovdiv.acad.bg (Received 24 August 1999; accepted in revised form 1 March 2000)
The equilibrium moisture contents were determined for vetch seeds using the gravimetric static method at 5, 20, 40 and 603C over a range of relative humidities from 0)110 to 0)877. The sorption capacity of the seeds decreased with an increase in temperature at constant relative humidity. The hysteresis e!ect was lower at higher temperatures. Five equations were applied for analysing the experimental data: modi"ed Chung}Pfost, modi"ed Halsey, modi"ed Oswin, modi"ed Henderson, and Guggenheim}Anderson}de Boer (GAB) equations. The modi"ed Oswin model was the most suitable for describing the relationships between equilibrium moisture content, relative humidity and temperature. Vetch seeds maintained a monolayer moisture content when stored at a relative humidity in the range 0)17}0)18 regardless of the temperature. 2000 Silsoe Research Institute
Notation a, b, b , c, c , d D e G E K E Q h ,h H P H PK M M G M K G M K N P R t ¹
model coe$cients degree of freedom randomness of residual mean relative error, % standard error of moisture model coe$cients relative humidity, decimal relative humidity corresponding to monolayer moisture content, decimal moisture content, % d.b. measured value of the equilibrium moisture content, % d.b. predicted value of the equilibrium moisture content, % d.b. monolayer moisture content, % d.b. number of data points level of signi"cance universal gas constant, 8)314 kJ/kmol K temperature, 3C temperature, K
1. Introduction A number of models have been previously suggested to describe the relationship between equilibrium moisture 0021-8634/00/080373#08 $35.00/0
content (EMC) and equilibrium relative humidity (ERH) (Van den Berg & Bruin, 1981). Some of them take into account the e!ect of temperature. The modi"ed Chung} Pfost (Chung & Pfost, 1967; Pfost et al., 1976), modi"ed Henderson (Henderson, 1952; Thompson et al., 1968), modi"ed Halsey (Halsey, 1948; Iglesias & Chirife, 1976a), modi"ed Oswin (Oswin, 1946; Chen & Morey, 1989) & Guggenheim}Anderson}de Boer (GAB) (Van den Berg, 1984) equations have been adopted as standard equations by the American Society of Agricultural Engineers for describing sorption isotherms (ASAE, 1995). The monolayer moisture content is of signi"cant importance to the physical and chemical stability of dehydrated materials with regard to their lipid oxidation, enzyme activity, non-enzymatic browning, and structural characteristics (Labuza et al., 1970). It can be determined from the equilibrium sorption isotherms by means of the twoparameter Brunauer}Emmett}Teller (BET) equation (Brunauer et al., 1938). Vetch (
373
2000 Silsoe Research Institute
374
N. D . M EN K OV
of the legume seeds have a substantial in#uence on their germination and longevity (Roberts, 1972; Ellis et al., 1988,1990; Vertucci et al., 1994). Therefore, it is necessary to investigate the equilibrium moisture content relationships of vetch seeds for various relative humidities and temperatures to enable the storage conditions for the seeds to be correctly speci"ed. The automatic control of these conditions requires a reliable mathematical description of the EMC/ERH using suitable models. The object of this work was to obtain the equilibrium moisture isotherms for vetch seeds at 5, 20, 40 and 603C and to "t a suitable model for describing the sorption characteristics.
2.3. Analysis of data The description of the relationship between equilibrium moisture content, equilibrium relative humidity and temperature was veri"ed according to the following models: Modi"ed Chung}Pfost
!a H "exp exp (!cM) P t#b Modi"ed Halsey H "exp P
(1)
!exp (a#bt) MA
(2)
2. Material and methods
1 Modi"ed Oswin H " P (a#bt/M)A#1
2.1. Material
Modi"ed Henderson H "1!exp [!a(t#b)MA] P (4)
Vetch seeds of the 666 cultivar were provided in 1998 by the Institute for Plant Genetic Resources, Sadovo, Bulgaria. The seeds were harvested 6 months in advance, sun-dried to approximately 12% d.b. and kept at room temperature and at a relative humidity of less the 0)55.
2.2. Procedure The equilibrium moisture content of the vetch seeds was determined at 5, 20, 40 and 603C. The static gravimetric method was applied (Wolf et al., 1985). For the adsorption process, seeds were "rst dehydrated in a desiccator over P O at room temperature for 20 days to a moisture content below 1% d.b. Samples for desorption measurements were "rst hydrated in a glass jar over distilled water at 43C for 20 days to approximately 30% d.b. Samples of 4$0)2 g were weighed in weighing bottles. The weighing bottles were then placed in hygrostats with ten saturated salt solutions (LiCl, CH COOK, MgCl , K CO , NaBr, Mg(NO ) , SrCl , NaCl, KBr, KCl), used to obtain constant relative humidities environments (Greenspan, 1977; Weisser, 1986). All salts used were of reagent grade. At high relative humidities (ERH'0)70), crystalline thymol was placed in the hygrostats to prevent microbial spoilage of the seeds (Wolf et al., 1985). The hygrostats were kept in temperaturecontrolled cabinets at 5, 20, 40 and 60$0)23C. Samples were weighed with an accuracy of 0)0001 g every 3 days. Equilibrium was acknowledged when three consecutive weight measurements showed a di!erence of less than 0)001 g. The moisture content of each sample was determined by the vacuum oven method (AOAC, 1990). The equilibrium moisture contents were determined by calculating the means of triplicate measurements.
(3)
abcH P GAB M" (5) (1!bH ) (1!bH #bcH ) P P P where M is the moisture content in % d.b., H is the P relative humidity as a decimal, a, b and c are model coe$cients, and t is the temperature in 3C. The parameters b and c in the GAB equation can be correlated with temperature using the following Arrhenius-type equations (Labuza et al., 1985):
h b"b exp R¹
(6)
h c"c exp R¹
(7)
where b , c , h , and h are coe$cients, ¹ is the absolute temperature in K, and R is the universal gas constant in kJ/kmol K. A non-linear regression program was used to "t the "ve models to the experimental data. The suitability of the equations was evaluated and compared using the mean relative error E as a %, standard error of estimate K E and randomness of residual e (Chen & Morey, 1989): Q G 100 , M !M K G G E " (8) K N M G G , (M !M K ) G E" (9) G G Q d D e "M !M K (10) G G G where M is the measured EMC value, M K is the value G G predicted by the model, N is the number of data points, and d is the degrees of freedom of regression model D (number of data points minus number of constants in the model). Data points in a plot of the residual values versus
M O I ST U RE SO R PT IO N I S O TH ER M S
375
the predicted EMC values should tend to fall in horizontal band, centred zero, displaying no systematic tendencies toward a clear pattern. If the residual plots indicate a clear pattern, the model should not be accepted (Chen & Morey, 1989). The two-parameter BET equation is valid for ERH(0)45 (Labuza et al., 1985): M cH K P BET M" (11) (1!H )(1!H #cH ) P P P where M is the monolayer moisture content in % d.b. K The M values for each temperature were calculated K from BET equation, following an algorithm described previously (Iglesias & Chirife, 1976b). Menkov et al. (1999) established for a large number of biological products that the dependence between M and temperature K was well described by a linear equation. A modi"cation of the BET model yields (a#bt)cH P (12) Modi"ed BET M" (1!H ) (1!H #cH ) P P P M "a#bt (13) K The coe$cients of Eqn (12) were determined directly, using a non-linear, least-squares regression programme on the basis of experimental data at ERH(0)45. The values of monolayer moisture content were determined using Eqn (13). The ERH value H corresponding to the PK monolayer moisture content was determined by Eqn (12) after putting M"M (Iglesias & Chirife, 1976b): K (c!1 H " (14) PK c!1
Fig. 1. Adsorption and desorption isotherms of vetch seeds at 53C: , adsorption; , desorption; , modixed Oswin equation [Eqn (3)]
1999; Menkov, 2000). The EMC values of vetch seeds are similar to those obtained from other legume seeds * cowpea (Pappas & Rao, 1987), ¸athyrus pea (Mazza & Jayas, 1991). The values of coe$cients E and E for the four, K Q three-parameter models (modi"ed Chung}Pfost, modi"ed Halsey, modi"ed Oswin, and modi"ed Henderson), are presented in Table 3 for adsorption and in Table 4 for desorption. The parameters for the GAB models are presented in Table 5. Analysis of the residuals for adsorption is presented in Fig. 3, and for desorption in Fig. 4. For the modi"ed Chung}Pfost (adsorption and desorption) and modi"ed Halsey equations (desorption), the residual plots indicated a systematic pattern which made
3. Results and discussion Figures 1 and 2 give the experimental data obtained after adsorption and desorption performed on vetch seeds at 5 and 603C, respectively. The sorption isotherms have an S-shaped pro"le, typical of legume seeds (Vertucci & Leopold, 1987; Pappas & Rao, 1987; Mazza & Jayas, 1991; Menkov, 2000). The hysteresis e!ect was distinctly expressed at 53C. At 603C the di!erences in the adsorption and desorption data were not statistically signi"cant (level of signi"cance P)0)05) for most of the experimental points. The experimental data for adsorption and desorption are presented in Tables 1 and 2, respectively. The EMC values decreased with an increase in the temperature at constant ERH. Similar trends for many seeds have been reported in the literature (Vertucci & Leopold, 1987; Pappas & Rao, 1987; Mazza & Jayas, 1991; Suthar & Das, 1997; Walters & Hill, 1998; Menkov & Dinkov,
Fig. 2. Adsorption and desorption isotherms of vetch seeds at 603C: , adsorption; , desorption; , modixed Oswin equation [Eqn (3)]
376
N. D . M EN K OV
Table 1 Equilibrium moisture content M in % d.b. obtained by adsorption at di4erent relative humidities Hr as a decimal and temperatures for vetch seeds 53C
203C
403C
603C
H, P dec.
M*, % d.b.
SDR
Hr , dec.
M, % d.b.
SD
Hr , dec.
M, % d.b.
SD
Hr , dec.
M, % d.b.
SD
0)113 0)245 0)336 0)431 0)589 0)635 0)757 0)771 0)851 0)877
5)2 7)7 9)2 10)6 13)0 14)0 17)7 19)2 23)1 24)8
0)06 0)22 0)17 0)08 0)19 0)14 0)14 0)18 0)14 0)25
0)113 0)231 0)331 0)432 0)544 0)591 0)725 0)755 0)817 0)851
4)8 7)6 8)8 10)3 10)9 11)9 14)5 16)9 21)2 22)6
0)10 0)11 0)19 0)21 0)13 0)07 0)13 0)17 0)21 0)29
0)112 0)201 0)316 0)432 0)484 0)532 0)658 0)747 0)794 0)823
4)1 5)5 7)7 8)4 8)7 9)8 12)8 15)6 16)7 18)8
0)08 0)13 0)18 0)24 0)09 0)05 0)18 0)07 0)11 0)16
0)110 0)160 0)293 0)432 0)440 0)497 0)580 0)745 0)789 0)803
3)6 4)6 5)8 7)3 7)5 8)3 9)5 12)9 14)1 14)5
0)05 0)10 0)08 0)24 0)17 0)25 0)17 0)13 0)13 0)12
* Mean of three replications. R Standard deviations based on three replications.
these equations unsuitable. The residuals obtained by all the other models denoted uniformly scattered points in residual plots. The modi"ed Oswin model had the lowest E and E values for adsorption and the lowest E value K Q K
for desorption compared to the other models. For description of the equilibrium isotherms of vetch seeds the modi"ed Oswin model is recommended. The GAB model is the second best model.
Table 2 Equilibrium moisture content M in % d.b. obtained by desorption at di4erent relative humidities Hr as a decimal and temperatures for vetch seeds 53C
203C
403C
603C
H, P dec.
M*, % d.b.
SDR
Hr , dec.
M, % d.b.
SD
Hr , dec.
M, % d.b.
SD
Hr , dec.
M, % d.b.
SD
0)113 0)245 0)336 0)431 0)589 0)635 0)757 0)771 0)851 0)877
6)5 9)8 10)8 12)2 15)5 17)1 19)0 21)2 23)3 29)2
0)09 0)07 0)18 0)16 0)08 0)22 0)21 0)11 0)16 0)25
0)113 0)231 0)331 0)432 0)544 0)591 0)725 0)755 0)817 0)851
5)5 8)0 9)8 11)1 12)1 13)0 17)2 21)7 23)0 24)5
0)14 0)20 0)13 0)12 0)10 0)21 0)29 0)06 0)21 0)21
0)112 0)201 0)316 0)432 0)484 0)532 0)658 0)747 0)794 0)823
4)5 6)4 7)8 9)8 10)0 10)5 13)5 16)9 17)4 20)2
0)16 0)13 0)21 0)02 0)12 0)17 0)13 0)12 0)19 0)16
0)110 0)160 0)293 0)432 0)440 0)497 0)580 0)745 0)789 0)803
3)7 4)7 6)0 7)8 7)8 8)5 10)0 14)1 15)4 17)0
0)06 0)18 0)20 0)07 0)06 0)24 0)20 0)04 0)23 0)11
* Mean of three replications. R Standard deviations on three replications. Table 3 Estimated values of coe7cients a, b, c; mean relative error Em, in % and standard error of moisture Es of three-parameter models for adsorption Estimated values
Parameter Modixed Chung}Pfost a b c E ,% K E Q
418)9 68)2 0)176 8)07 1)29
Modixed Halsey 4)302 !0)010 1)916 5)65 0)69
Modixed Oswin
Modixed Henderson
11)87 !0)057 2)48 3)79 0)58
0)00025 56)42 1)489 9)97 1)27
377
M O I ST U RE SO R PT IO N I S O TH ER M S
Table 4 Estimated values of coe7cients a, b, c; mean relative error Em, in % and standard error of moisture Es of three-parameter models for desorption Estimated values
Parameter Modixed Chung}Pfost a b c E ,% K E Q
345)9 45)8 0)165 6)42 0)97
Modixed Halsey 4)498 !0)015 1)859 6)46 1)54
Modixed Oswin
Modixed Henderson
13)77 !0)083 2)65 4)32 0)85
0)00017 43)08 1)685 8)18 1)17
Fig. 3. Residual plots of xve models for the adsorption data of vetch seeds
378
N. D . M EN K OV
Table 5 Estimated values of coe7cients a, b0, c0, h1, h2; mean relative error Em, in % and standard error of moisture Es of the GAB model
Adsorption Desorption
a
b
c
h
h
Em , %
Es
6)68 8)16
0)413 0)360
0)0011 0)0009
1655)4 1825)7
24191 24114
5)23 5)49
0)68 0)74
The values of monolayer moisture content obtained by the standard procedure for adsorption and desorption at di!erent temperatures, are shown in Fig. 5. There is also a hysteresis e!ect with respect to the monolayer moisture content. The M values decreased with the increase in K
temperature. The values for the coe$cients a, b and c of Eqn (12) for adsorption are 6)85, !0)0397 and 21)19, respectively; and for desorption are 7)91, !0)042 and 24)12, respectively. Figure 5 shows a comparison of the monolayer moisture content values obtained by the
Fig. 4. Residual plots of xve models for the desorption data of vetch seeds
M O I ST U RE SO R PT IO N I S O TH ER M S
379
References
Fig. 5. Ewect of temperature on the monolayer moisture content for: (a) the Brunauer}Emmett}Teller (BET) model [Eqn (11)]; , adsorption; , desorption; and (b) the modixed BET model [Eqn (12)]; , adsorption; , desorption
standard procedure [Eqn (11)] and by direct procedure [Eqns (12) and (13)]. It can be noted that there is a close agreement between standard and direct procedures. The H value does not depend on temperature since the PK coe$cient c in Eqn (12) does not depend on the temperature. Despite the hysteresis e!ect, the values obtained for H are similar for adsorption and desorption (0)18 PK and 0)17, respectively).
4. Conclusions The equilibrium moisture content of vetch seeds (cultivar 666) have been determined by the static gravimetric method at four temperatures. The sorption capacity of vetch seeds decreased with an increase in temperature at constant relative humidity. The hysteresis e!ect was lower at higher temperatures. The experimental data were "tted to "ve models. The modi"ed Oswin model was the most suitable for describing the relationship between the equilibrium moisture content, the equilibrium relative humidity and temperature. Vetch seeds showed a monolayer moisture content when stored at relative humidity about in the range 0)17}0)18 regardless of the temperature.
Acknowledgements This study was conducted with the kind support of the National Research Fund * Bulgaria.
AOAC (1990). O$cial Methods of Analysis (15th Edn.). Association of O$cial Analytical Chemists, Washington, DC ASAE (1995). Standard D245.5. ASAE, St. Joseph, MI Aydogdu L; AcikgoK z E (1995). E!ect of seedling rate on seed and hay yield in common vetch (
380
N. D . M EN K OV
Oswin C R (1946). The kinetics of package life. III. Isotherm. Journal of the Society of Chemical Industry, London, 65, 419}421 Pappas G; Rao V N M (1987). Sorption isotherms of cowpeas from 253C to 70 C. Transactions of the ASAE, 30, 1478}1483 Pfost H B; Mourer S G; Chung D S; Milliken G A (1976). Summarizing and reporting equilibrium moisture data for grains. ASAE Paper No. 76}3520, St. Joseph, MI Roberts E H (1972). Storage environment and the control of viability. In: Viability of Seeds (Roberts E H ed), pp 14}58. Chapman & Hall, London Suthar S H; Das S K (1997) Moisture sorption isotherms for karingda [Citrullus lanatus (Thumb) Mansf ] seed, kernel and hull. Journal of Food Process Engineering, 20, 349}366 Thompson T L; Peart R M; Foster G H (1968). Mathematical simulation of corn drying * a new model. Transactions of the ASAE, 11, 582}586 Van den Berg C (1984). Description of water activity of foods for engineering purposes by means of the GAB model of sorption. In: Engineering and Foods (McKenna B M ed), pp 119}131. Elsevier, New York
Van den Berg C; Bruin S (1981). Water activity and its estimation in food systems: theoretical aspects. In: Water Activity: In#uences on Food Quality (Rockland L B; Stewart G F eds), pp 1}61. Academic Press, London Vertucci C W; Roos E E; Crane J (1994). Theoretical basis of protocols for seed storage III. Optimum moisture contents for pea seeds stored at di!erent temperatures. Annals of Botany, 74, 531}540 Vertucci C W; Leopold A C (1987). Water binding in legume seeds. Plant Physiology, 85, 224}231 Walters C; Hill L M (1998). Water sorption isotherms of seeds from ultradry experiments. Seed Science Research, 8, 69}73 Weisser H (1986). In#uence of temperature on sorption isotherms. In: Food Engineering and Process Applications (Le Maguer M; Jelen P eds), Vol. 1, pp 189}200. Elsevier, New York Wolf W; Spiess W E L; Jung G (1985). Standardization of isotherm measurements (COST-project 90 and 90 bis). In: Properties of Water in Foods in Relation to Quality and Stability (Stimatos D; Multon J L eds), pp 661}679. Martinus Nijho! Publishers, Netherlands