State Diagram of Date Flesh Using Differential Scanning Calorimetry (DSC)

Abstract

The state diagram of date flesh was developed by measuring its freezing points, glass transition temperatures, maximal-freeze-concentration condition ( and ), and solute melting points (or decomposition temperature) by Differential Scanning Calorimetry (DSC). The freezing curve and glass transition lines were developed using Clausius-Clapeyron equation by incorporating concept of unfrozen water, and Gordon-Taylor equation, respectively. The developed state diagram of date flesh can be used in determining its stability during storage as a function of temperature and moisture content (such as, frozen and dried conditions) as well as in designing drying and freezing processes.

Introduction

State diagram is the map of the different states of a food as a function of water or solids content and temperature. The main advantage of drawing map is in identifying different states of a food, such as freezing point and glass transition, which helps 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 and moisture content for processing. The different components of a state diagram, such as freezing curve, glass line, maximal-freeze-concentration conditions are discussed as follows. The equilibrium or initial freezing point is one of the most important thermodynamic properties of a frozen food required for the prediction of thermal and physical properties because of the discontinuity exhibited at that point. Accurate freezing point data can also be used to calculate or determine the other properties such as effective molecular weight, water activity, bound, free, and frozen water, enthalpy below freezing, and construction of state diagram.1 Knowledge of freezing point is important for the analysis of freezing and thawing processes. Freezing point data can be used to ascertain chemical purity whether a sample differs from a natural or desired condition, i.e., detecting milk adulterated with water.1 Freezing point is also needed to estimate the freezing time using Plank's or similar form of equation. Recently there is an attention to other structural properties, such as glass transition, end point of freezing, maximal-freeze-concentration condition, solute melting point (or decomposition temperature), structural changes, and fraction of unfrozen water in foods due to its wide importance and applications in the food processing (i.e., freezing and drying) and food's stability during storage as a function of temperature and moisture content.2 3 4 Thus it is important to measure and model these properties.

Melting point of solute is important to know when food goes thru a higher temperature during processing, such as baking, frying, and extrusion cooking. In the literature there is very negligible information available for the melting or crystallization of solute(s) in foods. When multiple solutes present in a mixture like food, multiple melting points (if individual solutes do not interact) or single melting point (if all solutes interact and act as a single solute) or decomposition temperature (if individual solutes are involved in chemical reactions and forming other compounds) may present. The terminology used in the glass transition concept is discussed as follows. Glass transition is a nature of second-order time-temperature-moisture dependent transition, which is generally characterized by a discontinuity in physical, mechanical, electrical, thermal, and other properties of a material. In case of complex multi-component mixture, such as foods the discontinuity occurs with in a range of temperature. Glasses are not crystalline with a regular structure, but retain the disorder of the liquid or amorphous state. In kinetic terms, glass temperature is defined as the temperature at which the viscosity of a material reaches 10¹³–10¹⁴ Pa s and the molecular diffusion rate is in the orders of years. Usually in case of foods the modulus reached to 10⁸–10¹⁰ Pa. The state diagram is commonly used to identify different state boundaries in a material. In the state diagram in Fig. 1, the freezing line (ABC) and solubility line (BDK) are shown in relation to the glass transition line (EFG). The point F (, ) lower than (point C) is a characteristic transition (maximal-freeze-concentration condition) in the state diagram. The water content at point F or C is the unfreezable water (1−). Unfreezable water mass fraction is the amount of water remaining unfrozen even at very low temperature. In the region AHB, the phases present are ice and solution. Below point B, first crystallization of solute occurs, thus HBCI region transforms to three states; ice, solution, and solute crystal. Water having the ability to form ice does not exist right side of point C (, end point of freezing with maximal-freeze-concentration condition) and then the solution is transformed to rubber state. The maximal-freeze-concentration condition could be achieved using slow cooling and/or annealing of the samples, which allows the complete (i.e., maximum) formation of ice. The region ICFJ contains ice, rubber, and solute crystal. The point F is the , below this point rubber state is transformed to glass state, thus region JFG contains glass, ice, and solute crystal.

Figure 1. State diagram for solution. AB: freezing curve, BDL: solubility curve, B: eutectic point, EFG: glass transition line, JF: glass transition by slow or equilibrium cooling, T _gs : glass transition temperature of solids, T _gw : glass transition of water, : end point of freezing for maximal-freeze-concentration condition, : glass transition for maximal-freeze-concentration condition, : solids mass fraction at maximal-freeze-concentration condition, T _u : eutectic point (solutes crystallization), LD: or decomposition temperature line.

The most common method used to determine glass transition is the differential scanning calorimetry (DSC) that detects the change in heat capacity occurring over the transition temperature range. Other useful and some times more sensitive methods include thermomechanical analysis (TMA), dynamic mechanical analysis (DMA), and dynamic mechanical thermal analysis (DMTA).3 4 Differential scanning calorimetry is widely used to identify the characteristic changes in the state diagram. The DSC thermogram for the samples having solids content right side of F is relatively simple. In this case the samples do not form ice during cooling, the value is a glass-rubber transition T _g . A DSC thermogram in case of food samples containing ice is shown in Fig. 2 and different changes of states are marked on the diagram.5 The melting of ice endotherm is shown as D, two transitions as A and B, and an overshoot as C. The shift A is the glass transition of the branched chains (or more mobile) of polymer, and B is the glass transition before melting endotherm (, point F and , point C in Fig. 1) is the characteristic glass transition (i.e., when ice is formed during cooling process) at the end of freeze concentration. The transition B is due to the backbone of a large polymer or less mobile component. The two transitions were also observed in samples containing two solutes.6 Other proposed concept for solution with single solute is: it is the result of formation of a solute-crystal-rich, un-equilibrated phase trapped around or within the rapidly nucleated ice crystals, and/or solute inclusion within the ice crystals itself.7 The exothermic overshoot as shown as C could be due to enthalpic relaxation for differences in free volume of glass/ice during freezing or freezing of trapped water or trapped solute in the matrix. This phenomenon can be avoided by isothermal holding (annealing). Standard procedure for using DSC to measure and has not been developed. The reported procedures differ in cooling rate, warming rate, holding times-temperatures, annealing conditions, and sample size.8 These parameters can affect the degree to which end point of freeze-concentration is attained. Usually the annealing time and temperature as well as the cooling rate need to be optimized in order to determine and . Annealing appeared to be less critical for simple systems than for complex systems and for those samples with limited solubility. Optimum annealing conditions are required for accurate measurement of the maximal-freeze-concentration condition.

Figure 2. DSC thermogram showing transition 1 (marked A), transition 2 (marked B), exothermic overshoot (marked C), melting of ice (marked D), apparent and end point of freezing condition.

In the literature, glass transitions of pure components are more commonly reported than the real foods, which are complex multi-components mixtures. The glass transition temperatures of freeze-dried strawberry9 and cabbage10 were measured as a function of moisture content. State diagram of apple slices was developed by measuring glass transitions, freezing curves, and maximal-freeze-concentration condition with DSC method.5 Similarly the state diagram of dates was developed by measuring glass transitions of samples containing unfrozen water with dynamic oscillation method, and freezing points by cooling curve method.11 It is not easy to use the rheological methods below unfrozen water content due to the complexity of the physico-chemical process for water and solute crystallization, glass transition, and exothermic peak. Moreover, it is not simple to determine the maximal-freeze-concentration conditions from rheological measurement. Thus DSC studies were targeted for thorough studies of the complex process, which could provide a fundamental physics of the different states in date flesh.

The objective of this study was to develop the state diagram of dates by measuring glass line, freezing curve, solute melting points (or decomposition temperature), and maximal-freeze-concentration condition ( and ) by DSC method. More emphasis was given on the optimum cooling rate and annealing time.

Materials and Methods

Materials

Mature dates of Khalas variety were harvested in September from the date trees grown at the Agricultural Experiment Station of the Sultan Qaboos University and were stored at −40°C until used. The stored sample was thawed at room temperature before experimental use. The moisture content of the harvested dates (FS) was measured gravimetrically using an oven at 105°C for at least 18 h of drying and was found to be 28.4% (wet basis). The average length of the major and minor axis of mature dates was 35 ± 1, 18 ± 1, and 14 ± 0.8 mm, respectively. Dimensions were measured with a caliper. Average mass of the fruit was 8.5 ± 0.5 g. Pitted dates (cut into half in longitudinal direction) were stored in air-sealed glass jars that had reached equilibrium relative humidity with supersaturated salt solutions. The temperature of equilibration and duration were 20°C and 4 weeks, respectively. The salts used to prepare solution were: LiCl, CH₃COOK, MgCl₂, K₂CO₃, Mg(NO₃)₂, NaBr, SrCl₂, KCl, and K₂SO₄. The water activity of the samples could be varied from 0.113 (mass fraction of water, X _w : 0.138) to 0.985 (X _w : 0.586) using the above salts and the equilibrated samples were identified as SE. A 5 mL beaker containing thymol was placed inside the jars of higher water activity to prevent mold growth during storage. Moisture content in the other samples (RS) was maintained at that level by drying the date flesh in convection drier at 80°C (for samples moisture content at and above 0.068) or 105°C (for sample moisture content below 0.068) or by adding predetermined water and mixing thoroughly. Commercial dried dates (CP) were collected from the local date processing factory as brand name Tomoor Al-Wadi (Nizwa).

Differential Scanning Calorimetry

The freezing point, solute melting point (or decomposition temperature), and glass transition of date samples at different moisture content were measured by differential scanning calorimetry (DSC Q10, TA Instruments, New Castle, Delware). Mechanical refrigerated cooling system was used to cool the sample up to −90°C. The instrument was calibrated for heat flow and temperature using n-hexane (m.p. −94°C; ΔH _m  = 151 J/g), distilled water (m.p. 0°C; ΔH _m  = 334 J/g), and indium (m.p. 156.5°C; ΔH _m  = 28.5 J/g). Aluminum pan of 30 µL, 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.

Glass Transition of Samples Containing Unfreezable Water

Cut samples of 10–20 mg from the harvested and equilibrated or dried date flesh placed in a sealed aluminum pan were cooled to −90°C at 5°C/min, and equilibrated for 10 min. After equilibration it was scanned from −90 to 60°C at a rate of 5 or 1°C/min with 0–1 h annealing at −38°C. Each thermogram was analyzed for the onset, mid, and end of glass transition. The average values of 3–9 replicates were obtained. Standard deviation was used to identify the variability or error in the experimental measurements in the case of freezing point, solute melting point, and glass transition temperature.

Glass Transition and Freeing Point of Samples Containing Freezable Water

Glass transition and ice formation in samples containing freezable water is more complicated process and appropriate procedure must follow for these samples. Cut samples of 10–20 mg (moisture content, : 0.389 to 0.780) from the date flesh placed in a sealed aluminum pan were cooled to −90°C at 5°C/min, and equilibrated for 10 min. It was then scanned initially from −90 to 40°C in order to initial assessment of the thermogram and to locate T _g , and end point of freezing (i.e., apparent ). In the literature it was mentioned that annealing is necessary in order to achieve maximal-freeze-concentration condition (i.e., real and ) and eliminate the exothermic peak if present. In these experiments annealing time was varied from 0 to 1 h at  − 1 and optimum-annealing time was considered when melting thermogram showed no significant variation. The procedure was as follows: sample was cooled to −90°C at 5°C/min, heated at 5°C/min to  − 1, annealed from 0 to 1 h at  − 1, cooled at 5°C/min to −90°C, and scanned from −90°C at 5, 1, or 0.5°C/min to 40 or 60°C in order to determine actual and . This procedure was similar to Roos12 and Bai et al.5 In the cases of very concentrated samples the exothermic peak after glass transition could be avoided, but it was difficult to separate second glass transition from the melting endothermic peak. In this case scanning was done at optimum-cooling rate determined as 0.5 or 1°C/min.

The freezing point could be considered as the temperature at endothermic peak or at the point of maximum slope of the endothermic peak. In these experiments both exothermic peak and maximum slope were presented as initial or equilibrium freezing point. The latent heat of ice melting or freezing was estimated from the area of the melting endotherm. The average values of 3–5 replicates were obtained.

Solute Melting Point

Cut samples of 10–20 mg from date flesh placed in a sealed aluminum pan. Sealed sample was then cooled to −20°C at 5°C/min, and equilibrated for 10 min, then scanned from −20 to 220°C at a rate of 5°C/min. For completely dried sample problem of leakage or moisture loss during heating was absent. In case of wet samples it is difficult to achieve leak proof when heated especially above 100°C due to creation of high pressure inside the pan. In this case, drops of araldite were used to join the pan sealing in order to avoid leakage. The pan was left for overnight to solidify araldite. Separate experiment with araldite alone showed that it started to soften above 160°C, thus there was no confirmation of the leak proof above that temperature. Each thermogram was analyzed for the peak as solute melting point (or decomposition) from endotherm(s) and change in enthalpy was estimated from the area.

Results and Discussion

Glass Transition of Samples Containing Unfreezable Water

The glass transition temperature was determined from the DSC heat flow curves as shown in Fig. 3. Similar thermograms were also observed by Bai et al.5 in case of apple containing unfreezable water. The onset T _gi and final T _ge points of transitions were obtained by extrapolating the side and base lines. All thermograms for samples at and below moisture content 0.325 (: 0.675) showed only one transition and no formation of ice from water. Table 1 shows the effect of cooling rate and annealing time on the glass transition temperatures. In case of samples containing 0.325 moisture content (: 0.675) annealing time of 0–1 h and cooling rate 1 or 5°C affect the transition (p < 0.05). The maximum variation was observed as 2.3°C, thus glass transition of the samples containing unfreezable water were determined at a heating rate 5°C/min without annealing, and presented in the Table 2. In the literature it is most common to use scanning rate at 5°C/min for measuring the glass transition of foods. As expected glass transition temperature increased with the increasing solids content as shown in Table 2.

Table 1 Effect of annealing time and cooling rate on the glass transition temperature of the equilibrated samples containing unfrozen water content (: 0.675 and a _w : 0.755)

r c (°C/min)	AT (h)	N	T gi (°C)	T gp (°C)	T ge (°C)
5	0.0	7	−71.5 (0.5)	−68.3 (0.6)	−65.4 (0.5)
5	0.5	1	−71.9	−67.8	−64.8
5	1.0	1	−73.1	−69.4	−66.9
1	0.0	3	−72.9 (0.3)	−69.3 (0.2)	−66.9 (0.4)
1	0.5	1	−73.8	−70.0	−67.6

AT: Annealing time, N: number of replicates.

Table 2 Glass transition temperature above unfrozen water content when there is no formation of ice (without annealing and cooling rate 5°C/min)

Sample	N	a w	X s	T gi (°C)	T gp (°C)	T ge (°C)
SEa	7	0.755	0.675	−71.5 (0.5)	−68.3 (0.6)	−65.4 (0.5)
FS	1	0.717	0.716	−51.3	−54.7	−58.1
SE	1	0.570	0.782	−43.7	−46.4	−49.9
SE	1	0.544	0.802	−34.6	−38.2	−42.6
SE	1	0.432	0.821	−26.3	−29.8	−34.3
CP	1	—	0.832	−23.7	−29.3	−35.6
SE	1	0.331	0.880	−13.8	−17.2	−32.6
SE	1	0.231	0.851	−13.9	−20.3	−24.9
SR	1	0.113	0.862	−19.6	−24.3	−27.8
SR	5	—	0.889	−17.2 (2.9)	−23.3 (1.8)	−28.4 (2.0)
SR	3	—	0.927	29.2 (2.2)	32.7 (2.8)	35.6 (6.4)
SR	4	—	0.932	29.8 (3.7)	33.2 (2.3)	35.9 (1.2)
SR	9	—	0.969	33.9 (3.1)	36.4 (2.4)	38.5 (1.9)
SR	1	0.000	1.000	62.8	69.2	76.2

^aData from Table 1.

Figure 3. DSC thermogram of date sample containing unfrozen water ( is 0.325).

The glass transition temperature of foods and biological materials is commonly modeled by the following equation proposed by Gordon and Taylor13:

where T _g is the T _gi , and T _gs and T _gw are the glass transition temperature of mixture, solids, and water, respectively, and k is the Gordon-Taylor parameter. The onset of transition (T _gi ) was considered the glass transition of dates and fitted with Gordon-Taylor equation. The glass transition of pure water was considered −135°C for the nonlinear regression of Gordon-Taylor equation,14 and the values of T _gs and k for Khalas variety were found to be 63.8°C and 4.0, respectively. Kasapis et al.11 estimated the values of T _gs and k as 57.4°C and 3.2, respectively for mature dates of Barni variety. The predicted value of k = 4 for dates is similar to the literature values of 4.7 for strawberries, 5.3 for horseradish,15 and 3.59 for apple.5 The variation was expected due to the difference in chemical compositions. The values of T _gp and T _gi for 0.186 moisture content (: 0.814) samples are shown in Fig. 4 as a function of cooling rate. It shows that decreasing cooling rate decreased the glass transition and the values of T _gi decreased from 32 to 26°C (change 6°C) when cooling rate decreased from 20 to 5°C/min. Similarly in case of sugar-κ-carrageenan mixture equilibrated at 65% relative humidity, Kasapis et al.16 also observed a decrease of around 20°C in glass transition when cooling rate decreased from 30 to 10°C/min.

Figure 4. Effect of heating rate on the glass transition ( is 0.186).

Glass Transition of Samples Containing Freezable Water

A typical DSC thermogram of sample having moisture content at 0.498 (: 0.502) is shown in Fig. 5 without annealing. It shows freezing exotherm during cooling (F in Fig. 5), glass transitions 1 (A in Fig. 5) and 2 (B in Fig. 5), and melting endotherm (D in Fig. 5). The initial point of ice melting (i.e., end point of freezing) in the Fig. 5 is identified as apparent (initial point of melting) and (initial point of glass transition B). Optimum annealing condition was obtained when the sample is held at  − 1 for a considerable period of time, allowing a maximum amount of ice to be formed, and leading to a maximally concentrated solid matrix of moisture content equivalent to . The optimum annealing condition and cooling rate are shown in Table 3. A DSC thermogram of annealed sample is shown in Fig. 6. The difference between end point of freezing (apparent and ) and maximal-freeze-concentration condition (actual and ) could be understand in Fig. 7 when cooling curve is plotted as a function of cooling rate. Sample starts cooling from point a, and b is the initial freezing point. Curve bc is the slowest possible cooling conditions. This slowest cooling rate can be achieved by controlling the cooling rate as well as applying annealing process. Curve bf is the fastest cooling rate showing no nucleation of ice. Samples containing moisture content within 0.498 and 0.611 (: 0.502 and 0.389) showed similar DSC thermograms as Fig. 6.

Figure 5. DSC thermogram of sample containing freezable water ( is 0.498).

Figure 6. DSC thermogram of 30 min annealed sample at  − 1 ( is 0.498 and cooling rate 5°C/min).

Table 3 Freezing point and glass transition of date flesh as a function of moisture content

								Transition 1			Transition 2
Sample	r c (°C/min)	AT (h)	X s	T F a (°C)	T F b (°C)	(ΔH)sample (kJ/kg)	(°C)	T gi (°C)	T gp (°C)	T ge (°C)	T gi () (°C)	T gp (°C)	T ge (°C)
RS	5	0.5	0.220	−1.8 (0.1)	−4.1 (0.8)	172 (9)	−26.1 (1.7)	−61.4 (0.6)	−57.6 (0.8)	−54.5 (0.5)	−44.2 (0.4)	−42.6 (0.6)	−41.5 (0.5)
RS	5	0.5	0.298	−3.2 (0.6)	−5.5 (0.6)	151 (2)	−34.9 (2.9)	−60.6 (1.3)	−58.4 (0.6)	−56.0 (1.6)	−44.3 (0.3)	−42.2 (0.2)	−40.0 (0.6)
RS	5	0.5	0.360	−4.9 (1.2)	−7.2 (1.3)	122 (6)	−31.0 (1.5)	−60.7 (1.9)	−58.4 (0.7)	−54.9 (0.5)	−44.7 (0.2)	−42.9 (0.1)	−40.7 (0.2)
ES	5	0.5	0.414	−7.8 (0.8)	−10.8 (0.3)	87 (8)	−40.9 (1.7)	−60.9 (0.8)	−57.1 (1.0)	−54.8 (1.8)	−46.3 (1.9)	−43.3 (0.5)	−41.4 (0.4)
RS	1	0.5	0.511	−12.6 (0.7)	−15.2 (0.5)	59 (3)	−37.1 (1.7)	−59.7 (1.1)	−56.9 (1.4)	−54.4 (0.5)	−46.4 (1.6)	−44.3 (1.8)	−42.4 (2.1)
ES	1	0.5	0.541	−18.3 (2.2)	−20.2 (1.8)	55 (7)	−38.9 (0.9)	−58.5 (1.5)	−55.3 (1.2)	−54.0 (0.9)	−44.1 (1.5)	−39.7 (0.8)	−39.4 (1.1)
RS	1	0.5	0.589	−20.3 (2.3)	−23.4 (2.8)	41 (9)	−37.9 (2.7)	−62.6 (1.7)	−58.6 (2.0)	−56.1 (1.2)	−44.8 (1.7)	−42.6 (1.9)	−39.9 (2.7)
ES	1	0.5	0.611	−22.0 (1.1)	−25.6 (1.3)	27 (8)	−43.6 (1.7)	−63.4 (1.4)	−59.3 (1.8)	−57.0 (0.9)	−46.4 (1.5)	−45.4 (1.7)	−43.8 (1.2)

Note: r _c (cooling rate) and AT (annealing time) are the determined optimum conditions.

^aMaximum peak.

^bMaximum slope.

A typical DSC thermogram of sample having moisture content below 0.389 (: 0.611) is shown in Fig. 8. In this case, freeze-concentration of the sample results in a temperature-dependent equilibrium between the ice crystals and the unfrozen solution surrounding them. At sufficiently low temperature, this freeze-concentrated unfrozen phase reaches sufficient viscosity to become glassy. In this case, the thermogram became more complicated by showing no freezing exotherm during cooling, and showing overshoot or exotherm (C in Figs. 8 and 9), ice melting enotherm (D in Figs. 8 and 9). It is difficult to identify the glass transition in this case. Figure 10 showing annealing at  − 1 can eliminate the exothermic peak, and shows two glass transitions, one condensed with the ice melting endotherm D (Fig. 9). The two glass transitions can be clearly separated by using optimum annealing time, as well as reducing the cooling rate further. In this condition, transitions 1 and 2, as well as maximal-freeze-concentration condition ( and ) can be determined (Fig. 10). The exothermic peak was also observed in case of sucrose solution without annealing,17 for beef muscle, and egg white (Simatos et al.18). In case of egg white, Simatos et al.18 also observed two glass transitions one at −85°C and another at −46°C. However, they did not present the explanation of the two transitions. They were more concerned on characterizing the types of bound water. Table 3 shows the glass transitions 1 and 2, freezing point, enthalpy change of sample during ice melting, and maximal-freeze-concentration condition ( and ). Goff et al.7 also observed freeze-concentrated sucrose solutions had two glass-like transitions. The glass transition-like nature of transition 1 may have resulted from the formation of a sucrose-rich, un-equilibrated phase trapped around or within the rapidly nucleated ice crystals, and/or solute inclusion within the ice crystals themselves. Such a phase may arise from concentration gradient and limited diffusion at the crystal interface. This phase relaxed at a higher temperature than did the bulk unfrozen phase, resulting in the two-step glass transition. When this phase disappeared from maturation or perfection of ice crystals or equilibration of the unfrozen phase (up to 5 weeks), then the transitions seen in heat flow curve lost its glass transition like characters.7 In case of date flesh with 1°C/min and 0.5 h annealing was unable to remove the transition 1. Further, experiments need to be targeted with much more equilibration and/or two cycles cooling-heating instead of only one cycle. The solute melting point (i.e., eutectic) was missing in the thermogram during heating. To the best of author's knowledge, in the literature the eutectic point was also missing from the thermogram. It was not clear why this could not be traced even for pure components. This also needs further investigation. The freezing points based on endothermic peak (point a in Fig. 5) and maximum slope of endothermic peak (as point b in Fig. 5) are presented in Table 3. It is more reasonable to consider maximum peak of the endothermic peak as the initial or equilibrium freezing point and used for model development and state diagram. Similarly the maximum peak was considered as the initial or equilibrium freezing point for foods when DSC was used.19 20

Figure 7. Freezing curve as a function of cooling rate.

Figure 8. DSC thermogram of sample of is 0.389.

Figure 9. DSC thermogram of 30 min annealed sample indicating elimination of exothermic peak or overshoot ( is 0.389 and heating rate 5°C/min).

Figure 10. DSC thermogram of 30 min annealed sample at  − 1 and heating rate 1°C/min showing the clear separation of transitions 1 and 2.

The theoretical Clausius-Clapeyron equation was used to estimate the freezing point of dates, and the equation can be written as:

where δ is the freezing point depression (T _w  − T _F ), T _F is the freezing point of food (°C), T _w is the freezing point of water (°C), β is the molar freezing point constant of water (1860 kg K/kg mol), λ _w is the molecular weight of water, is the initial solids mass fraction, and E is the molecular weight ratio of water and solids (λ _w / λ _s ). The model parameter E was estimated using SAS nonlinear regression and found to be 0.147 for date flesh. From the value of E, the effective molecular weight of solids was 122. The Clausius-Clapeyron equation is limited to the ideal solution (i.e., for a very dilute solution). Theoretical models can be improved by introducing parameters for nonideal behavior when fraction of total water is unavailable for forming ice. The unfreezable water content B can be defined as the ratio of unfrozen water even at very low temperature to the total solids.21 Equation (2) can be modified based on this concept as:

The model parameters E and B were estimated using SAS nonlinear regression22 and found to be 0.129 and 0.053 (in wet basis, unfreezable water,  = 0.050; and solids content,  = 1–0.050 = 0.95), respectively. The mean square error from experimental data using Eqs. (2) and (3) are 5.5 and 4.6, respectively. This indicates that accurate prediction can be done using Eq. (3) when considering the accuracy. However, found 0.95 is physically unsound although mathematical accuracy in prediction of freezing point is achieved. In the case when parameters are estimated by nonlinear regression using experimental data, Eq. (3) is transformed to the empirical nature although it is based on the physics. This is one of the generic problems when theoretical based model is extended to fit the experimental data.

A typical DSC thermogram showing the melting of sucrose is shown in Fig. 11 and the melting point is 191.6°C and enthalpy is 118 kJ/kg compared to the literature values 188°C and 120 kJ/kg, respectively.1 Figure 12 shows a rugged melting endotherm of completely dried date flesh. The melting peak was at 191°C and enthalpy is 192 kJ/kg. Figure 13 shows two endotherms when moisture was at 0.246 (: 0.754). The lower temperature one is due to the melting of sugars in date flesh and other one due to the melting (or decomposition) of high molecular weight solutes, such as pectin and cellulose as well as water evaporation. Moisture content below 0.186 showed only one endotherm at high temperature. It is difficult to confirm whether it is the solute melting point of solids or moisture evaporation, or decomposition, or all processess happening at the same temperature. Solute melting points decreased with the decrease of solids content. Further studies need to be targeted in this direction.

Figure 11. DSC thermogram showing melting of sugar.

Figure 12. DSC thermogram showing melting of completely dried date flesh.

Figure 13. DSC thermogram showing melting of sugar and melting of other solutes at higher temperature for dates at is 0.246.

The values of are shown in Table 3 as a function of solids content and found that it decreases with the increase of solids content. Actual and are considered (lowest values with scan for sample having low moisture with freezing water) as the −43.6 and −46.4°C, respectively. Kasapis et al.11 did not measure the and determined the by extending the cooling curve to the glass transition by maintaining the similar slope. This procedure does not give accurate estimation since it considers that and contain different moisture content. In reality the and should contain the same moisture content since there is no ice formation to the right side of . Figure 14 shows the state diagram of date flesh incorporating the cooling curve, glass transition curves, and maximal-freeze-concentration condition, solute melting points. Curve AC 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 C is the shown as in the Fig. 14. The intersection of vertical extrapolation of the point P on the glass transition curve at 0.762 (point F in Fig. 14), which is the . At this stage, no water crystallize to ice in concentrated solutes of date flesh. The water content at point F is known as the unfreezable water, which for date flesh is 0.238 (). Table 3 shows a trend that increase in solid content decreased the . However, solids contents at 0.360 or lower increased significantly the values of .

Figure 14. State diagram of dates. AC: freezing curve, EFG: glass line, and solute melting points.

Various methods have been used to predict unfrozen water content ( or ) in the maximal-freeze-concentration state. The method proposed by Levine and Slade23 was based on determination of ΔH _m for a 20% solution, which reportedly provides a fast method to determine approximately the unfrozen water content. The unfreezable water content can be calculated from the amount of ice:

(ΔH _m )_sample is enthalpy change during melting of ice in the sample as shown in Table 3, (ΔH _m )_water is the latent heat of melting of ice (334 kJ/kg). Simatos et al.18 plotted (ΔH _m )_sample with the moisture content, unfreezable water content was calculated from the linear relationship extending to zero (ΔH _m )_sample. Alternatively a linear regression for date samples can be developed as (Fig. 15):

Figure 15. Change of enthalpy during melting of solids as a function of moisture content.

The values of can be estimated from the above equation as 0.32 when (ΔH _m )_sample is equal to zero. The values of unfrozen water content calculated from different methods are given in Table 4. The procedure by Eqs. (4) and (5) give error due to two reasons24: (i) Enthalpy of pure water (heat of fusion) is a function of temperature and this can give error up to 10% if freezing point depression is 5–10°C, (ii) Heat represented by the area under the curve is a combination of heat of fusion of ice plus sensible heat taken by freshly melted water. Table 4 indicates that unfrozen water estimated from the ice-melting endotherm varied with the initial solution concentration. Similar variation was also observed in case of fructose,25 and sucrose.26 Roos27 used enthalpy change of the sample as well as latent heat of ice melting to construct similar to the Fig. 15, and found completely different values of unfreezable water content. Ablett et al.25 mentioned that calculation of unfreezable water by extending freezing line to glass temperature curve is the most reliable method. The unfreezable water content from the freezing point prediction model (Eq. (3)) is not a reliable method although it gives accurate prediction for freezing point.

Table 4 Unfrozen water content by different methods

		Unfrozen water ( )
Sample		Eq. (4)			Eq. (5)	Eq. (3)	State diagram
RS	0.780	0.265	0.290a (0.026)	0.320	0.050	0.238
RS	0.702	0.247
RS	0.640	0.274
ES	0.586	0.326
RS	0.489	0.312
ES	0.459	0.294
RS	0.416	0.293
ES	0.389	0.308

^aAverage value from Eq. (4); value in parenthesis is the standard deviation.

Conclusion

The freezing points of dates flesh were varied from −1.8 to −22.0°C when solids content changed from 0.22 to 0.611, respectively. Experimental data were modeled using Clausius-Clapeyron equation by incorporating the concept of unfreezable water. The model parameters E (molecular weight ratio of water and solids) and B (unfreezable water fraction) were estimated as 0.129 and 0.053, respectively. The glass transition temperatures were varied from −71.5 to 62.8°C when solids content varied from 0.675 to 1.00, respectively. The values of T _gs and k were estimated using Gordon-Taylor equation as 63.8°C and 4.0, respectively. The values of and (maximal-freeze-concentration) were found to be −43.6 and −46.4°C, respectively, and the unfreezable water content was found 0.238 from the state diagram.

Acknowledgment

The project was funded by Sultan Qaboos University (Internal Grants IG/AGR/FOOD/00/02 and IG/AGR/BIOR/02/03), Muscat, and His Majesty's Research Trust Fund (SR/AGR/PLNT/01/01), Sultanate of Oman. The author would like to thank Tomoor Al-Wadi, Nizwa for supplying a sample of their product.