Journal of Food Engineering 99 (2010) 92–97
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State diagram of dates: Glass transition, freezing curve and maximal-freeze-concentration condition Nejib Guizani a,*, Ghalib Said Al-Saidi a, Mohammad Shafiur Rahman a, Salwa Bornaz b, Ahmed Ali Al-Alawi a a b
Department of Food Science and Nutrition, College of Agricultural and Marine Sciences, Sultam Qaboos University, P.O. Box 34, Al-Khod 123, Muscat, Oman Ecole Supérieure des Industries Alimentaires de Tunis, 58 Avenue Alain Savary, 1003 Tunis, Tunisia
a r t i c l e
i n f o
Article history: Received 8 November 2009 Received in revised form 1 February 2010 Accepted 3 February 2010 Available online 10 February 2010 Keywords: State diagram Glass transition Differential scanning colorimetry Maximal-freeze-concentration condition Dates
a b s t r a c t The state diagram of Deglet Nour dates was developed using freezing curve, glass transition line, and maximal-freeze-concentration condition. Freezing points and glass transition temperature were measured by differential scanning calorimetry (DSC) as a function of water content. Freezing points were fitted to the Clausius–Clapeyron equation adjusted with un-freezable water, and glass transition was fitted to the Gordon–Taylor model. Glass transition decreased with a decrease in solids content, confirming the plasticizing effect of water on date solids. Freezing point data indicated the temperature when ice formed and dates would be most stable in terms of its deterioration if it can be stored below its glass transition. Maximum-freeze-concentration conditions was found as X 0s (characteristic solids content) = 0.78 g/g sample, with the characteristic temperature as T 0g (characteristics glass transition) = 48 °C and T 0m (characteristic end point of freezing) = 38.2 °C. These characteristics indicated that 0.22 g/g sample water in date was un-freezable (i.e. bound with solids or unable to form ice). The developed state diagram can be used in determining the stability of dates during storage as a function of temperature and moisture content. Moreover, it can be used to determine optimum drying and freezing conditions. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The fruits of the date palm Phoenix dactylifera, are one of the important agricultural commodities in North-African countries, the Middle East, and Asia. Global production of date fruits exceeds six million metric tonnes annually in the world (Boudries et al., 2007). Tunisia and Algeria are the traditional Deglet Nour suppliers for France and Europe. In 2004, 110,000 tons of dates were produced in Tunisia which represents 7% of the whole fruit tree production and 16% of the value of agricultural exportations (GID, 2004). Edible dates pass through four distinct stages of ripening termed in arabic – Kimri, Khalal, Rutab and Tamr – and used to represent, respectively, the immature green, the mature full colored, the soft brown and the hard raisin-like stages of development (Ahmed et al., 1995). Dates are generally consumed as fresh or may be processed into various products such as date paste, syrup or powder which are used as ingredients in cookies or cake manufacturing. The date is a sugar-rich and low moisture material. The sugars are of the reducing or non-reducing type and on average the sugar content is 0.8 g per g dry matter (Belarbi et al., 2000). Presently, considerable proportion of the dates exported by North-African * Corresponding author. Tel.: +968 24141256; fax: +968 24413418. E-mail address:
[email protected] (N. Guizani). 0260-8774/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2010.02.003
countries does not fulfill the FAO/WHO Codex Alimentarius. The water content is variable, with differences as high as 25% (Belarbi et al., 2000). The biochemical and microbial stabilities of foods such as the date strongly depends on the state of water, which affects the characteristics of the products. Thermal analysis determines different phases and states of foods as a function of water content and temperature (Rahman, 2004, 2006). State diagram is the map of different states of a food as a function of water or solids content and temperature (Rahman, 2006). The main advantages of drawing a map are to help in understanding the complex changes when food’s water content and temperature are changed. It also assists in identifying food’s stability during storage as well as selecting a suitable condition of temperature content for processing (Rahman, 2006). It has been reported in the literature that foods can be considered very stable at the glassy state, since below glass transition temperature compounds involved in deterioration reactions take months or even years to diffuse over molecular distances and approach each other to react (Slade and Levine, 1991). Glass transition temperature is related to the viscosity-related structural transformations of biological materials, such as crystallization, stickiness, collapse, elasticity, shrinkage and molecular mobility (Rahman, 2006; Kantor et al., 1999). In the literature, glass transitions of pure components are more commonly reported than the real foods, which are more complex multi-components
N. Guizani et al. / Journal of Food Engineering 99 (2010) 92–97
mixtures. The glass transition temperature values of tuna (Rahman et al., 2003), king fish muscle (Sablani et al., 2007), strawberry (Roos, 1987), garlic (Rahman et al., 2005), grapefruit (Fabra et al., 2009) and dates (Kasapis et al., 2000; Rahman, 2004) were presented in the literature. There is scanty information in the literature on the structural properties of date ingredients in relation to temperature of processing and level of addition to product formulations. Clearly successful use of date ingredients (syrup, pectin, fiber) in the development of novel appealing formulations will confer substantial wealth to cultivators and manufacturers alike (Kasapis et al., 2000). The overall objective of this study was to develop the state diagram of Deglet Nour dates by measuring glass line (glass transition temperature versus solids content), freezing curve (freezing point versus solids content), and maximal-freeze-concentration conditions (T 0g , T 0m and X 0s ) and other related characteristics by DSC method. 2. Material and methods 2.1. Raw materials Deglet Nour samples were bought from a local market (Tunis, Tunisia), transported the same day by air to Oman and stored at 4 °C until used for experiments. Biochemical analyses were run to provide data on water content, dry matter, protein, fat, and ash (AOAC, 1996). Total carbohydrates were calculated by difference. 2.2. Sugar analysis Approximately 20 g of de-seeded date fruits were added to 80 g of de-ionized water and boiled for 10 min to inactivate enzymes. After the inactivation treatment, the weight of water was checked. Any loss in water (due to evaporation) was compensated with fresh de-ionized water. Then, the contents were transferred into a high-speed laboratory blender and homogenized. The homogenate was analyzed immediately for individual sugar. The free sugars were determined by HPLC according to the technique of Myhara et al. (1998) with minor modifications. Homogenized date samples (20 g) were refluxed with 80 ml of 85% aqueous ethanol for 15 min. The liquid extract was collected and the residue was refluxed again with 75% aqueous ethanol. Again, the liquid part was collected and combined with the previous extract. The combined extracts were evaporated to dryness in a rotary evaporator. The dry sugar residues were dissolved in 50 ml of 1:1 acetonitrile:water solution and filtered through a 0.45 lm cellulose acetate filter. The HPLC analysis was carried on an Agilent 1100 (Agilent, USA) system, equipped with a Supelcosil™ LC-SI column (250 mm 4.6 mm ID, particle size 5 lm, Supelco Park, Bellefonte, PA, USA) and a differential refractive index detector (Agilent RID 1100). A sample size of 20 ll of the dissolved sugar residue was injected in the system and eluted by 75:25 acetonitrile:water solution at a flow rate of 1 ml/min. The temperature of the column compartment as well as the temperature of the detector flow cell was maintained constant at 40 °C throughout the analysis. 2.3. Samples equilibration at different water activity Degle Nour samples (approximately 5 g) were placed in open weighing bottles and stored in air-sealed glass jars (at 20 °C) while maintaining equilibrium relative humidity with saturated salt solutions by keeping a layer of crystal at the bottom. The salts were: LiCl, Ch3COOK, MgCl2, K2CO3, NaBr, and SrCl2 (BHD, Laboratory supplies, Poole, England). Relative humidity values for these solutions were obtained from the compilation of Spiess and Wolf
93
(1987). The samples were equilibrated until a constant mass was achieved. A test tube containing thymol was placed inside the jars of higher water activity to prevent mold growth during storage (Guizani et al., 2008). The equilibration took around 6 weeks. The equilibrated samples were placed in air tight glass bottles and stored at 20 °C until used for DSC analysis. The moisture content of equilibrated samples was measured by oven drying method at 105 °C for 24 h. 2.4. Differential scanning calorimetry (DSC) The freezing point, glass transition and deterioration temperature of Deglet Nour samples at different relative humidity values were measured by DSC (DSC Ql0, TA Instruments, New Castle, Delware, USA). Mechanical refrigerated cooling system was used to cool the sample up to 90 °C. The instrument was calibrated for heat flow and temperature using distilled water [melting point (m.p) = 0 °C; DHm = 334 J/g] and indium [m.p. = 156.5 °C; DHm = 28.5 J/g]. Aluminum pans of 30 lL, which could be sealed with lid, were used in all experiments with an empty sealed pan as reference. Nitrogen at a flow rate of 50 mL/min was used as a carrier gas. Samples (containing un-freezable water) of 5–10 mg of date were placed in an aluminum pan and then sealed. The sealed pan with samples were cooled to 90 °C at 5 °C/min, and equilibrated for 10 min. After equilibration, it was scanned from 90 °C to 50 °C at a heating rate of 10 °C/min. Each thermogram was analyzed for the onset, mid, and end of glass transition, melting (or denatured) endotherm, and decomposition characteristics. At least five replicates were performed for each sample. A different procedure was used for samples containing high water (moisture content: 0.07–0.90 g/g sample) having freezable water. Samples of 5–10 mg of the powder in a sealed aluminum pan were cooled to 90 °C at 5 °C/min, and equilibrated for 10 min. The sample then scanned from 90 °C at 10 °C/min to 50 °C in order to determine freezing point and apparent maximal-freeze condition [(T 0m )a and (T 000 g )a]. After knowing the apparent (T 0m )a and (T 000 g )a, samples were scanned similarly with 30 min annealing at [(T 0m )a 1] °C, in order to measure actual Tm and Tg. The initial or equilibrium freezing point was considered as the point of maximum slope of the endothermic peak. For the materials showing wide peak of ice melting on the DSC thermogram, the point of maximum slope corresponds well with the initial freezing point estimated from well established cooling curve method (Rahman 2004). The latent heat of ice melting (or freezing) was estimated from the area of the ice melting endotherm. The average values of three replicates were obtained. 3. Results and discussion 3.1. Chemical composition The date fruits from Deglet Nour variety were analyzed for moisture, ash, protein, and total and individual sugars. The water content of mature dates was 21.43 g/100 g sample. Carbohydrates were the main fractions of date solids (74.11 g/100 g dry solids). Simple sugars represented 74 g/100 g total carbohydrates with sucrose being the main sugar followed by glucose and fructose, 19.12, 18.35 and 17.50 g/100 g date flesh, respectively. Protein, fat and ash were, respectively, 2.47, 0.31 and 1.68 g/100 g dates. 3.2. Water sorption isotherm Fig. 1 shows the desorption isotherms of Deglet Nour dates at 25 °C (Present work, series 5), Allig dates at 40 °C (Bellagha et al.,
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0.7
Water ( w.b.)
0.6 0.5
Series1
Series3
Series2
Series4
Series5
0.4 0.3 0.2 0.1 0 0
0.2
0.4
0.6
0.8
1
1.2
Water activity Fig. 1. Water desorption isotherms of different cultivars of dates.
2007, series 1), Khalas dates (Rahman and Al-Farsi, 2005, series 3) and Kentichi and Bahri varieties at 25 °C (Belarbi et al., 2000, series 3 and 4, respectively). Desorption isotherms of the different varieties of dates showed less pronounced sigmoidal shapes. This shape is characteristic of high-sugar foods (Saravacos et al., 1986). At low relative humidity, dates adsorbed a low amount of water because of the water sorption of high molecular components. However, for aw higher than 0.5, a larger amount of moisture is adsorbed because of the dominant water sorption of water. A slight difference in the sorption behavior for the different varieties was also observed. This difference may be due to differences in the composition of dates and more specifically to the sugar content. For instance, Kentichi has the lowest sugar content (0.68 g/g, Bellagha et al., 2007) compared to Allig (0.86 g/g, Bellagha et al., 2007) and to Deglet Nour (0.741 g/g, present study). It is clear from Fig. 1 that for the same water activity, Kentichi has the lowest content compared to Deglet Nour, Allig dates.
3.3. Thermal transitions of date flesh containing un-freezable water The glass transition temperature of samples of low moisture content (i.e. high solids) having presumably un-freezable water was determined from DSC heat flow curve as shown in Fig. 2. This figure presents only portion of the thermogram around the glass transition temperature of date flesh at a one moisture level (0.17 g water/g date flesh). The onset of Tgi and final Tge points of transitions were obtained by extrapolating the side and base lines. All thermograms for samples at and below moisture content 0. 22 g/g sample (Xs = 0.78 g/g sample) showed one transition and no formation of ice during cooling and no ice melting endotherm during heating. Similar thermograms were also observed by Sereno et al. (1998), Bai et al. (2001) and Rahman et al. (2005). The glass
transition temperature of foods depends mainly on the quantity of water, constituents and molecular weight of solutes present in the food. The glass transition temperatures in foods did not show sharp shift in the thermogram line instead it occurred over a range of temperatures (Rahman, 2006). This is shown in Table 1 which gives the initial (Tgi), mid (Tgm) and end points (Tge) of the glass transitions of date flesh obtained from thermogrms of dates with high solids contents (0.790–0.908 g solids/g date flesh). The glass transition temperature was considered as the Tgi, when sample remained into completely glass form (Rahman, 2006). Water content had clearly an influence on glass transition temperatures of date flesh. Table 1 shows the increase in glass transition with the increase of solids content. The Tgi decreased from 13.8 to 48.7 °C as water content of date flesh increased from 0.09 to 0.21 g water/g date flesh. The depression in glass transition with increasing water content is the result of the plasticizing effect of water on the amorphous constituents of the matrix (Rahman et al., 2005). Water is a well-known plasticizer with a Tg between 135 and 139 °C, and generally for most materials, the higher the moisture content, the lower is the Tg (Collares et al., 2004; Rahman, 1995; Roos, 1993). Dates are a mixture of several components containing water, carbohydrate, protein, and fat as 21.43, 74.1, 2.47 and 0.31 g/100 g date flesh, respectively. The major sugars found in Deglet Nour are sucrose, fructose and glucose representing, respectively, 19.12, 18.35 and 17.50 g/100 g date flesh. Dates flesh exhibited glass transitions temperatures and thermograms similar to those reported for sucrose, glucose and fructose solutions (Ablett et al., 1993a,b; Simperler et al., 2006; Roos, 1993; Arvanitoyannis et al., 1993). Syamaladevi et al. (2009) reported glass transitions temperatures and thermograms for raspberries that are similar to glucose and fructose, the two main sugars found in the fruit. Spyropoulos et al. (2010) identified that sucrose played complex role in structure building macromolecules. Sucrose up to 0.15 g/g sample increased the miscibility of the mixtures, but increasing sugar content further showed increasing incompatibility between the polysaccharide and protein macromolecules (i.e. opposite effect). Comparison of glass transition values with those reported earlier in the literature is made difficult since some researchers reported transitions at mid point only (Tgp) while others reported transitions at the onset (Tgi). Adding to this difficulty, annealing temperature and times are not consistent. Clarification of these thermal transitions in frozen systems is a priority since new technologies and processes that attempt to use this approach must rely on the position of T 0g under specific conditions (Goff and Sahagian, 1996). Since transition occurs within a relatively wide range of temperature, it is more reasonable to report the transitions as initial, mid and end points (Rahman, 2006).
3.4. Thermal transitions of dates containing freezable water Dates containing freezable water (50–93 g water/100 g dates) were scanned without annealing to identify the end point of freezTable 1 Glass transition and melting of Deglet Nour date (samples with no freezable water).
Fig. 2. Glass transition temperatures of date flesh equilibrated at 0.17 kg water/kg dates (scan rate 10 °C/min).
Xw
Glass transition Tgi (°C)
Tgp (°C)
Tge (°C)
0.092 0.150 0.160 0.170 0.180 0.190 0.210a
13.8 28.4 32.0 33.8 39.8 44.8 48.7
7.7 21.5 18.9 25.7 28.9 38.6 42.5
2.0 16.8 12.9 21.1 24.2 34.8 38.5
Note: DSC heating rate (10 °C/min). a Fresh dates.
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Temperature oC
20
Series1
Series2
0 Tm' = - 38.2 oC
-20 -40 -60
Xs ' = 0.78
-80 -100 0
0.2
0.4
0.6
0.8
1
Solids Mass Fraction Fig. 4. Plot of T 0m as a function of solids contents as measured by cooling curve (series 1) and differential scanning calorimetry (series 2).
250 Enthalpy change (kJ/kg)
ing or start of melting of ice crystals T 0m . The glass transition temperatures obtained were less noticeable before ice melting. In order to identify the maximal-freeze-concentration, dates were thus scanned with annealing for 30 min at T 0m 1. Several researchers have demonstrated that proper annealing protocols within a narrow temperature range between Tg and onset of melting T 0m are necessary to allow for delayed crystallization (Roos and Karel, 1991a,b; Sahagian and Goff, 1994; Ablett et al., 1992). However, some other reports showed that it is very difficult to form ice at concentrations above 70% solute without extensive annealing (long times) and/or temperature cycling and therefore it is virtually impossible to maximally freeze-concentrate within realistic time-frames (Franks, 1982; Le Meste and Huang, 1991; Izzard et al., 1991). Table 2 shows the initial freezing points (TF), glass transitions, end point of freezing (T 0m ), and enthalpy of ice melting (DHm) of date flesh determined from thermograms obtained for high water content samples. The TF decreased from 2.53 to 31.51 °C as total solids content (Xs) increased from 0.10 to 0.93 g solids/g date. The glass transition temperature (T 000 g ) in Table 2 is relatively independent of solids content at or above 0.60 g solids/ g date. Similar observations were reported by Rahman (2004) for date flesh, Rahman et al. (2005) for freeze–dried garlic powder, and Fabra et al. (2009) for grape fruits. Fig. 3 shows DSC cooling and heating thermograms for sample containing freezable water (0.70 g water/g date). The location of 0 000 T 000 g and T m are shown before start of the ice melting. The T g is defined as the glass transition of the rubbery portion of the solids matrix containing ice and un-freezable water. The T 0m is defined as the end of freezing, and below T 0m the sample cools without forming ice. The T 0m is unique to the product and is influenced by the molecular weight of total solids present in
200 150 100 50 0 0
0.2
0.4
0.6
0.8
1
Water Content, Xw (kg H2O/kg dates) Table 2 Glass transition and maximal-freeze-concentration conditions of Deglet Nour date. Melting of ice
Glass transition 2
Glass transition 1
Xs
TF (°C)
DHice (kJ/kg)
T 0m (°C)
T 000 g (°C)
Tgi (°C)
Tgp (°C)
Tge (°C)
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.82
2.53 4.74 6.77 6.22 11.21 18.91 33.25 27.18
195.50 149.83 110.50 124.80 96.54 62.01 29.34 39.13
8.19 10.99 15.27 14.04 21.84 31.31 35.56 38.49
11.73 17.37 18.79 19.18 25.71 42.63 37.12 41.35
n n n n 39.47 55.74 59.03 60.79
N N N N 37.42 51.23 53.46 54.20
n n n n 35.94 50.49 49.61 51.92
Note: DSC heating rate: 10 °C/min, n: not detected.
H eat F lo w (W /g )
10
Heating up to annealing
5 Tgp=-56.46
0
Cooling
Tg'''=-37.12 Tm'=-35.56
-5 -10
-20 -100
Tge=49.61 -80
foods. The T 0m of Deglet Nour decreased with increasing solids content; however, at solids content greater than 60% the change in value of T 0m is small (Table 2). Sopade et al. (2002), Rahman (2004) and Rahman et al. (2005) also found a decreasing trend of T 0m with increasing solids contents; the increase was small at solids contents’ greater than 40%. Fig. 4 shows a plot of apparent T 0m versus solids content as measured by DSC and cooling curve. The intersection of the horizontal lines with the average values of T 0m when these were nearly constant and extension of the freezing curve corresponded to the value of maximal-freeze-concentration condition as T 0m (Rahman, 2005). The T 0m of Deglet Nour dates was 38.2 °C at total solids 78%. The T 0m of Deglet Nour is in the range of sugars it comprises i.e. T 0m of sucrose, glucose and fructose (T 0m = 34 °C, 30 °C and 48 °C, respectively) (Roos and Karel, 1991a). The enthalpy of ice melting decreased as solids content increased. The enthalpy of ice melting (DHm) was plotted against water content to determine the quantity of un-freezable water (Fig. 5). A linear relationship was obtained from regression analysis as follows:
ðDHm Þsample ¼ 254:7X ow 44:9
Tgi=-59.03
-15
Fig. 5. Change in enthalpy of ice melting as a function of water content in dates.
-60
ð1Þ
Heating after annealing
TF =-33.25 -40
-20
0
20
40
60
o
Temperature ( C) Fig. 3. Typical thermogram of date flesh containing freezable water (0.90 g water/g date) (scan rate 10 °C/min).
The amount of un-freezable water obtained by extrapoling the line to DHm equal to zero was 0.18 kg water/kg date flesh (Fig. 5). This value is close to that reported by Rahman (2004) for Omani dates (0.2 g water/g date flesh). The quantity of un-freezable water observed for grapes, strawberries, garlic, pineapple and raspberry were 0.197, 0.184, 0.32, 0.30, 0.27 and 0.16 g water/g sample, respectively (Sa and Sereno, 1994; Roos, 1987;
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Fig. 6. State diagram of Deglet Nour dates showing freezing curve, glass transition line, and maximal-freeze-concentration condition (T 0m , T 0g , X 0s and other characteristics).
Rahman et al., 2005; Telis and Sobral, 2001; Syamaladevi et al., 2009; Silva et al., 2006). 3.5. State diagram Fig. 6 shows the state diagram of dates incorporating the cooling curve, glass transition and maximal-freeze-concentration condition. Curve AP represents the equilibrium between the solution and ice formed, and it has a negative gradient showing the expected decrease in the freezing point with increasing concentration of solids. The point P in Fig. 6 is shown as T 0m equal to 38.2 °C. The intersection of vertical extrapolation of the point P on the glass transition curve at 0.78 g/g sample (which was determined earlier as X 0s ) is point F in Fig. 6. At this point no water crystallizes to ice in concentrated solids of dates. The water content at point F is known as the un-freezable water, which is 0.22 g/g sample [X 0s = (1 Xuw)]. The T 0g is defined as the intersection of the vertical line on the glass line KFL, which is 48 °C (Fig. 6). Glass transition of dates should be expected to occur at an intermediate temperature for sucrose–glucose–fructose mixtures. T 0g values for freeze-concentrated sucrose, glucose and fructose solutions were published and ranged 32 to 46 °C for sucrose, 42 to 53 °C for fructose, 43 to 52 °C for glucose (Levine and Slade, 1992; Franks, 1985; Roos, 1992; White and Cakebread, 1966; Finegold et al., 1989; Orford et al., 1990), 31.2 and 50 °C for grapefruit (Fabra et al., 2009), and 40.1 and 58.8 °C for camu–camu fruit (Silva et al., 2006). The values of T 0m and T 0g for Omani Khalas dates were different from our values; they were 43.6 and 46.4 °C, respectively (Rahman, 2004). These differences could be attributed to the difference in the types of sugars present in each variety of dates and possibly other components. Glucose and fructose are the main types of sugars in Khalas (Myhara et al., 1998), whereas sucrose is the main type of sugar in Deglet Nour followed closely by glucose and fructose. Orford et al. (1990) found that the glass transition temperature of a carbohydrate depended strongly on molecular weight and less on its structure. Accordingly, the T 0g of Deglet Nour dates (high content of sucrose) would be higher than the T 0g of Khalas dates, which is not the case here. Thus, additional factors may have had an effect. Among these crystallinity is known to cause an increase in T 0g (Mizuno et al., 1998), and interactions of com-
pounds. In addition differences in defining T 0g on the state diagram could be another factor. In fact, the T 00g value reported by Rahman (2004) was determined as the intersection of the freezing curve to the glass line by maintain the similar curvature of freezing curve. This point is similar to the T 00g defined in this paper, which is equal to 42 °C (Fig. 6). In the literature, another point is determined by extending the AP line to the glass line by maintaining the same curvature of the freezing curve and is defined as T 00g (Sereno et al., 1998; Kantor et al., 1999; Kasapis et al., 2000; Rahman, 2006). In Fig. 6 it is defined as G (T 00g = 42 °C and X 00s = 0.82). The difference in the values of T 0m (38.2 °C) and T 00g (42 °C) is within the experimental error, thus are not significantly different for Deglet Nour dates. Similar differences were observed for garlic (Rahman et al., 2005). However, with tuna meat the difference could be more than 20 °C, indicating the dependence on product types (Rahman et al., 2003). The glass transition temperature of foods and biological materials is commonly modeled by the following equation proposed by Gordon and Taylor (GT) (1952):
Tg ¼
X s T gs þ kX w T gs X s þ kX w
ð2Þ
where Tg used here is the Tge; and Tgs and Tgw are the glass transition temperature of mixture, solids and water, respectively; k is the Gordon Taylor parameter and Xw and Xs are the mass fraction of water and solids (wet basis). Considering that the glass transition of pure water was 135 °C (Johari et al., 1987), the GT equation yielded Tgs and k values of 9.7 °C and 2.6, respectively. The k value obtained for Deglet Nour was in the range reported for other date varieties, 4.0 for Barni variety (Kasapis et al., 2000) and 3.2 for Khalas variety (Rahman, 2004). However the value of Tgs appears low taking into account that the range of Tgs values of sucrose, fructose and glucose are 52–70, 7–17.6 and 20–30.6 °C, respectively (Levine and Slade, 1992; Franks, 1985; Roos, 1992; White and Cakebread, 1966; Finegold et al., 1989; Orford et al., 1990). It is also low when compared to Tgs values reported by Kasapis et al. (2000) and Rahman (2004) and 4.0 for Barni variety (63. 4 °C) and for Khalas variety (57.4 °C), respectively. Similarly, in the case of grapefruit, Fabra et al. (2009) reported the values of k and Tgs as 4.11 and 34.5 °C, respectively.
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4. Conclusion The present investigation attempts to map out the melt, rubbery, and glassy states of Deglet Nour dates solids by means of a state diagram. The freezing points measured by DSC varied from 2.53 °C to 27.18 °C when solids content increased from 10% to 93%, respectively. The glass transition temperature decreased from 8.19 °C to 38.49 °C when solids content decreased from 91% to 78%, respectively. The state diagram provided an estimate of maximally freeze-concentrated solids at 0.78 g/g sample (X 0s ) with the characteristic temperature of end point of freezing (T 0m ) being 38.2 °C and the characteristic glass transitions T 0g and T 00g being 47 °C and 42 °C, respectively. The glass transition of dates containing un-freezable water indicated its (i.e. dry dates) stability region during its storage, whereas T 0m indicated the stability for the frozen dates. The un-freezable water in dates was observed as 0.22 g/g sample indicating the amount of reactive water.
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