Gordon-Taylor constant

Calculated using Gordon-Taylor equation with an intrinsic glass transition, 7 of 74°C (347 K) and - 139°C (135 K) for sucrose and water, respectively, and a Gordon-Taylor constant value of 0.13675. 

Tg dry represents the glass transition temperature of the (dry) solid, Tg,w the glass transition temperature of water, w the water content (wet-based) and k the so-called Gordon-Taylor constant. 

Gordon-Taylor Constant n This constant has been applied to polymer blends for the purpose of predicting the resultant glass transition temperature T mixing multiple polymers with different glass transition temperatures. A typical expression using the constant is... 

Glass transition temperature is one of the most important parameters used to determine the application scope of a polymeric material. Properties of PVDF such as modulus, thermal expansion coefficient, dielectric constant and loss, heat capacity, refractive index, and hardness change drastically helow and above the glass transition temperature. A compatible polymer blend has properties intermediate between those of its constituents. The change of glass transition temperature has been a widely used method to study the compatibility of polymer blends. Normally, the glass transition temperatme of a compatible polymer blend can be predicted by the Gordon-Taylor relation ... 

According to Gordon and Taylor constant k would be given by the relationship ... 

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. 

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... 

According to Simha-Boyer rule AaTg = constant and thus the Gordon-Taylor parameter can be expressed as ... 

Turning to polymer solutions, an identical equation to Wood s equation is the Gordon-Taylor equation, as written in Fig. 7.69 (Wj = Mj, 1 - M2 = Mj, etc.). This equation was proposed to account for the glass transition in case of volume-additivity of the homopolymers. If this condition holds, the constant k should be PiAa2/p2Aa, where p represents the densities and the Aa the change in expansivity at the glass transition of the homopolymers. 

A different equation results if one assumes that the product of the change in expansivity with the glass transition temperature, AaT, is a constant, known as the empirical Simha-Boyer rule AaT = 0.113. The well-known and simple Fox expression for the glass transition temperature results on insertion of the Simha-Boyer rule into the Gordon-Taylor equation. The Gibbs-Di Marzio and the Fox equations are easily generalized to SVT or pVT equations of state when assuming that the solution can be based on simple additivity of the homopolymer properties. 

To add effects of specific interactions, the Gordon-Taylor expression can be expanded into a virial expression, as in the Schneider equation, listed in Fig. 7.69 [30]. The variable W2c is the expansivity-corrected mass fraction of the Gordon-Taylor expression W2c = kW2 / (Wj + kWj). The Schneider equation can be fitted with help of the constants Kj and K2 to many polymer/polymer solutions, as is illustrated in Sect. 7.3.2. The parameter Kj depends mainly on differences in interaction energy between the binary contacts of the components A-A, B-B, and A-B, while Kj accounts for effects of the rearrangements in the neighborhood of the contacts. 

Plotting the glass transition temperatures of Fig. 7.73 as a function of concentration, yields Fig. 7.74. Only the Gordon-Taylor equation with a fitted constant represents the data. Similarly it is possible to fit with the Schneider equation with its two constants. Two additional equations, not in Fig. 7.69, are compared in Fig. 7.74 to the data one, is the Couchman equation, based on additivity of the products of ACp with the logarithm of T, the other uses a molar additivity of the logarithn of T. All equations without adjustable parameters do not fit the experimental data (o). 

The experimental values available for the constant Kn, in general, do not agree with those predicted by the considerations of Gordon and Taylor. Wood [7] suggested, therefore, to consider Kn as a characteristic parameter for the particular copolymeric system, not necessarily related to the A values of the homopolymers. 

A theoretical interpretation of the glass transition temperature of a copolymer is based on the assumption that the transition occurs at a constant fraction of free volume. Gordon and Taylor [9] assume that in an ideal copolymer the partial specific volumes of the two components are constant and equal to the specific volumes of the two homopolymers. The specific volume-temperature coefficients for the two components in the rubbery and glassy states are assumed to remain the same in the copolymer as in the homopolymers, and to be independent of temperature. The glass transition temperature Tg for the copolymer is then given by [10]... 

---