Glass transition curve

In systems as described above, the rate of cooling must be significantly faster than the rate of nucleation in order for a glass to be formed. Effectively, the system must be cooled rapidly through the crystallization zone of the state diagram bounded by the solubility curve and the glass transition curve. Systems that crystallize more rapidly than they can be cooled will not form glasses. 

Glass-transition curve of three model system formulations ( control, O sorbitol, glycerol) expressed vs. (a) water activity or (b) moisture content. Lines indicate the predicted values according to the Gordon-Taylor model (Sherwin and Labuza, 2003). 

The Tg curves for the water-maltodextrin-sucrose system was plotted using the expanded Gordon-Taylor model (Equation 21.1) for ternary systems, considering the variation in heat capacity for water (ACpi) equal to 1.94 J/g °C (Kalichevsky and Blanshard, 1993) and for sucrose (ACp2) equals to 0.60 J/g °C (Roos, 1993). The value for ACps of 0.24 J/g °C used here for maltodextrin MOR-REX 1910 was estimated from considering the value for k (the ratio of changes in the water and solid heat capacities at Tg) to be equal to 8.055. Table 21.1 shows the parameters used to determine the glass-transition curves for the maltodextrins, with and without additives (sucrose). 

Parameters Used to Determine the Glass-Transition Curves According to the Gordon-Taylor Model... 

The results obtained for the detachment of the maltodextrins RD-111 (Figure 21.4a) and MOR-REX 1914 (Figure 21.5b) confirmed the behavior found by Collares et al. (2004) for maltodextrin MOR-REX 1910. The conditions for the self-detachment of maltodextrins with different A4 followed the same pattern as the glass-transition curve of the corresponding material. The experimental points, however, are located underneath the curve, probably due to an overdrying during the sample collection procedures. For the maltodextrins RD-111 and MOR-REX 1910, self-detachment occurred in the temperature range of 15°C below the Tg curve, and for the maltodextrin MOR-REX 1914, the limits of temperature was 20°C. 

Glass-transition curves for maltodextrins with different molecular weights (a) 4759 g/mol, DE — 04 and (b) 957.5 g/mol, DE — 19, and experimental points at the moment of self-detachment of the film from a solid surface. 

The composition of the mixture influences the glass-transition phenomenon in a similar way. Figure 21.4 shows the glass-transition curves calculated for aqueous solutions of MOR-REX 1910 and sucrose. The proportion of sucrose was 5, 10, and 15% with respect to the solids content. The curves show the decrease in Tg with an increase in sucrose concentration, a behavior... 

Glass-transition curves (Gordon-Taylor model) for maltodextrin MOR-REX 1910 and sucrose. 

Glass-transition curves and self-detachment conditions for aqueous solutions of maltodextrin MOR-REX 1910 (a) maltodextrin + 5% sucrose, (b) maltodextrin + 10% sucrose, and (c) maltodextrin -I-15% sucrose. 

In Figure 21.5, the self-detachment conditions for aqueous solutions of the maltodextrin MOR-REX 1910 and sucrose at 5, 10, and 15% (dwb) are compared with the glass-transition curves calculated using the expanded Gordon-Taylor model (Roos, 1993). The self-detachment of the dried films of aqueous solutions of the maltodextrin MOR-REX 1910 and sucrose followed the same pattern of decreasing moisture content of the material with an increase in temperature as observed with the glass-transition data. This process occurred in a temperature range of 20°C below Tg, for 5,10, and 15% sucrose concentrations, as was observed by Collares et al. (2004) for maltodextrin MOR-REX 1910 without the addition of sucrose. 

The Tg plotted versus the product moisture content gives the glass-transition curve. If the melting temperature is also added to this plot, a state diagram is obtained. Complete state diagrams for some natural foods have been published, but they are still limited in number, being found only for onion, grape, and strawberry (Roos, 1987 Sa and Sereno, 1994), apple (Sa et al., 1999 Bai et al., 2001), pineapple (Telis and Sobral, 2001), persimmon (Sobral et al., 2001), and tomato (Telis and Sobral, 2002). 

The Gordon-Taylor model (Equation 58.1) for binary systems could well represent the glass-transition curve of the sugar matrix at — 0-90. The following parameters were calculated by nonlinear regression k = 3.76 and Tgg = 375.7 K, with = 0.996, using Tgj = 138 K (Inoue and Ishikawa, 1997). In Equation 58.1, Xg is the dry solids fraction and X is the water fraction of the material ... 

As expected, the melting temperature decreased with decreasing water content. The intersection of the extrapolated ice melting and glass-transition curves would be expected to occur at Tg (Slade and Levine, 1991). Other authors (Karel et al., 1994) consider that this intersection would occur at T[n, which corresponds to the lowest equilibrium melting point within the unfrozen matrix. Values of T[n were also included in Figure 58.3. 

A state diagram for freeze-dried plum was obtained and the Gordon-Taylor model could adequately represent the sugar matrix glass-transition curve. 

Relationship between Glass-Transition Curves and Sorption Isotherms for the Evaluation of Storage Conditions of Freeze-Dried Camu-Camu (Myrciaria dubia (Hbk) Mcvaugh) Pulp with and without Maltodextrin Addition... 

Relationship Between Glass-Transition Curves and Sorption Isotherms... 

Fig. 3.43 Phase diagram of the PCL/PS blend triangles homogeneous melt/PCL crystal coexistence curve, filled circles glass-transition curve, open circles spinodal, and squares binodal)...

In a number of cases, analysis of the thermal effects enables one to reveal additional iiiforiiialion of the state diagram the presence of a glass transition curve, the identification of the phase separation regions of both the amorphous and crystalline types in the same system (van Emmerik and Smolders, 1973b). However, the thermal effects of phase separation in polymer systems often turn out to be insignificant for reliable determination of the phase separation region (Papkov, 1981). 

Figure 5. InterrekttUmship of ass tnmsitions aid moistwe sorption isotherms of foods. At every condition to the of the glass transition curve,...

Another interesting fact is that the polymer samples prepared by compression molding did not show a glass transition (curve A), but when the sample was heated and cooled again (curves B and C) a glass transition was observed. This suggests that the intensity of the glass transition in the semicrystalline polymer is substantially... 

Effect of Pressure Pressure is one of the physical factors that often influences the glass transition, since polymeric products are frequently prepared by injection molding. Here, the skin-core effect needs to be mentioned that is, a thin surface layer of an injection-molded polymeric product solidified at a temperature different from that of the bulk. If the sample sohdi-fied at an elevated pressure, endothermic peaks would appear at the low-temperature side of the glass transition curve. These peaks shift to lower temperatures with increasing pressure. The DSC curves get rather complex, but little quantitative information can be extracted besides the fact that the sample was cooled under high pressure. 

The glass transition curve usually shows an enthalpy relaxation or hysteresis peak as well. The intensity of the hysteresis peak can be greatly increased if one anneals the glass just below the glass transition temperature or if the material was slowly cooled (see Section 2.7, on phase transitions in thermoplastic polymers). TTiis poses two problems (1) obtaining a comparative glass transition temperature and (2) evaluating the hysteresis behavior. 

Fig. 1.3 Typical glass transition curve and typical evolution of food product temperature during drying as a function of moisture content (DM dry matter).

For example, powdered milk products remain dry, free-flowing and stable when maintained below the glass transition temperature. However, if the powder picks up moisture from the air or experiences elevated storage temperatures, it may exceed the glass transition curve and become less stable (mbbery state). In this case, powdered milk would be likely to get sticky, and the powder would cake together. In a spray-dryer, operating parameters have to be chosen to ensure a rapid drying... 

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