Gordon-Taylor model

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... 

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

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

The glass-transition experimental data obtained with the DSC showed a great reduction in Tg with the increase in moisture content. In the water activity domain studied (0.11 < < 0.90), Gordon-Taylor model (Equation 62.2) was adequate to adjust the experimental data. In Equation 62.2, and are the mass fraction of solids and water, fc is a constant derived experimentally for the solid component, and Tg, Tgs, and Tgw are the glass-transition temperatures for the mixture, the bone-dry solid components, and pure water (— 135°C), respectively. The model parameters, estimated by nonlinear regression for freeze-dried camu-camu natural pulp... 

Parameters Estimated for Gordon-Taylor Model for Freeze-Dried Camu-Camu pulp... 

The GAB model (Equation 62.1) and Gordon-Taylor model (Equation 62.2) were combined to adjust the values of Tg as a fimction of water activity, resulting in Equation 62.3 proposed by Khalloufi et al. (2000) ... 

Theoretically miscible polymer blends will show Tg values that are intermediate between those of the parent polymers. They follow such models as the Fox or Gordon-Taylor relationships (18,19). However, in the case of HPL/PVA blends, the Tg data did not follow any of these well known models, and Tg values above those of the parent polymers were observed (10). The quotient of the experimental blend-Ttf divided by the predicted (Fox) Tg consistently rose above 1.00 for blends exceeding 5% HPL content (10). This indicates molecular interactions between HPL and PVA. An... 

Water plasticized the food models and caused a substantial decrease of the glass-transition temperature. The Gordon-Taylor equation was successfully fitted to experimental glass transition temperatures of the three model systems, as shown in Figure 53.2b. The constant, k, for the Gordon-Taylor equation was found to be 7.6 0.8 for lactose/reactant systems, 7.2 0.7 for lactose/trehalose/reactant systems, and 7.9 0.9 for trehalose/reactant systems. The three model systems had corresponding glass-transition behaviors, which were typical of lactose-based dairy products. The critical water contents at 23°C obtained from Tg data for lactose/reactant, lactose/trehalose/reactant, and trehalose/reactant systems were 7.0, 7.4, and 7.1 g/100 g of dry solids, respectively. 

Equation (C.3) is applicable for the Gordon-Taylor volume additivity model, and... 

The T of polymer blends can be related to the blend composition by different equations, as shown in Table 12.2. The T of miscible blends of poly(p-dioxa-none) with poly(vinyl phenol) (PPDO/PVPh) [74], as studied using the Fox [75], Gordon-Taylor [76], Couchman-Karasz [77] and Kwei [78] models, showed that the experimental data lay below the Fox equation, suggesting that the free volume of the blends was larger than predicted, assuming free volume additivity. On the other hand, the Gordon-Taylor and the simplified Kwei equations fitted the experimental T values appropriately. Other studies have shown that the Ta of SAN/PMMA blends was also effectively approached by the Gordon-Taylor relationship [79,80]. 

In the Gordon-Taylor equation (4) Tg is the glass temperature of the copolymer or of the miscible polymer blend, respectively, w and Tg. are the weight fractions resp. glass temperatures of the components. K is a model specific parameter, i.e., ifoT = P ... 

In 1993, the journal SAR and QSAR in Environmental Research was launched by Gordon and Breach to focus on all the important works published in the field and to provide an international forum for the rapid publication of SAR (Structure-Activity Relationship) and QSAR models in (eco) toxicology, agrochemistry, and pharmacology. Today, the journal, which is now owned by Taylor Francis and publishes three times more issues per year, continues to promote research in the QSAR field by favoring the publication of new molecular descriptors, statistical techniques, and original SAR and QSAR models. This field continues to grow very rapidly... 

The earliest models to appear were developed by Karrig, Wood arrd Gordon arrd Taylor. These models were based on qirite simple expressiorrs such as that of Fox, derived from that of Gordon and Taylor ... 

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