Gordon glass transition temperatures

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 ... 

Figure 7.4 shows the glass transition temperatures of PVDF/PMMA blends as a function of PVDF content after a melt process. The results " show agreement with Gordon-Taylor relation up to about 40 wt %, which is much higher than the 20wt % obtained from the annealed blends. This is certainly a result of the increased content of amorphous PVDF matrix in melt-processed blends compared with annealed blends. 

Glass-transition temperatures of the three diblocks and the two homopolymers are plotted against isoprene content in Figure 3. The values plotted in Figure 3 were determined by TMA at a heating rate of 5°C/min. The points fall near a straight line which can be described by a simplified version of the Gordon-Taylor equation (20) ... 

Blends of PCL with PVC were shown to exhibit only one glass-transition temperature (Tg), which for blends quenched from the melt could be represented as a function of composition by the Gordon-Taylor Tg equation. By similar criterion, the PCL blends with NC were shown to be compatible for the composition range 0-50% NC by weight. With higher concentrations of NC, both thermal and mechanical testing indicated that multiple amorphous phases were present, even though the films were clear. 

Figure 7.9. Glass transition temperature of gelatinized WMS as a fiinetion of moisture content compared to the Gordon-Taylor predictions (Reprinted from Carbohyd. Polym., 51, Zimeri and Kokini, Phase transitions of inulin-waxy maize starch systems in limited moisture environments, pp. 183-190, Copyright (2003), with permission from Elsevier.)...

The glass transition temperature of amorphous multicomponent mixtures can be used to determine the miscibility of the components. If the mixture is miscible, then a single glass transition temperature is usually obtained. Various equations can be used to predict the glass transition temperature of miscible mixtures. Examples include the Gordon-Taylor equation [Eq. (11)] or the Fox-Flory equation [Eq. (12)]. 

The glass-transition temperature curve of the maltodextrin RD-111, MOR-REx 1910, and MOR-REX 1914 were obtained using the Gordon-Taylor equations for binary systems, according to the procedure described by Collares et al. (2004). 

Water acts as a plasticizer for soy flour (Yildiz and Kokini, 2001). Therefore, increase in water content will plasticize the matrix causing an increase in available free volume for molecular transport. Moisture diffusion as a result will be effected from the water activity of the system. The relationship between moisture content and a can be established using the moisture sorption isotherm (MSI) of soy flour. The glass transition temperature is a very important concept in the diffusion process. At the vicinity of the glass-transition temperature the diffusion process increases at a higher rate. Figure 46.1 shows the plasticization effect of moisture on soy flour and Gordon-Taylor prediction of Tg vs. moisture content (Yildiz and Kokini, 2001). 

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... 

FIGURE 3.18 The variation of the glass transition temperature of binary systems with composition, presented in terms of the Gordon-Taylor relationship (a) phenobarbital-salicin and (b) antipirin-phenobarbital. (Reproduced from Fukuoka, E., Makita, M., and Yamamura, S., Chem. Pharm. Bull., 37, 1047, 1989. With permission.)... 

From these values, one may calculate and compare the effective glass transition temperature of the resin as a function of diluent concentration. Gordon et a1. have recently derived an expression relating the glass temperature of a polymer-plasticizer mixture to the glass temperatures of the components on the basis of the configurational entropy theory of glass formation (4). 

Fig. 6.4-6 Effect of water on the glass-transition temperature of several carbohydrates, calculated with the Gordon-Taylor equation [B.108]...

Because water plasticizes hydrophilic food components, their glass transition is strongly dependent on water content. The effect of water on the glass-transition temperature of several amorphous carbohydrates, calculated with the Gordon Taylor equation [B.79], is depicted in Fig. 6.4-6. Within the range of the materials shown, Tg decreases with lower average molecular weight and/or increased concentration of plasticizer (water). 

Fig. 21. Entropy versus log-temperature diagram for the hard-sphere model. The solid curves give the computer simulation values for the supercooled fluid, glass, and crystal. The dashed curves have the following bases (a) a calculation from the virial equation using the known first seven coefficients and higher coefficients obtained from the conjectured closure (the plot corresponds quite closely with that calculated from the Camahan-Starling equation ) and (i>) an extrapolation of higher temperature behavior such as that used by Gordon et al., which implies a maximum in the series of virial coefficients. The entropy is defined in excess of that for the ideal gas at the same temperature and pressure. Some characteristic temperatures are identified 7, fusion point 7 , upper glass transition temperature T/, Kauzmann isoentropic point according to closure virial equation.

Figure 15.4 Glass transition temperatures of emidsion-polynierized styrene-butadiene copolymers of various compositions (Gordon and Taylor [16])...

Blends of poly(trimethylene terephthalate) (PTT) and PEN are miscible in the amorphous state over a wide range of eompositions. This is evidenced by a single, composition-dependent glass transition temperature (7 ). The variation of the Tg with composition can be predicted by the Gordon-Taylor equation, with the fitting parameter being 0.57. 

In Fig. 46 the dependences of glass transition temperature Tg, determined by the thermomechanical method, on formal contents cform are shown for the indicated copolymers. As one can see, the dependences Tg(cform) course is different for these copolymers. For APESF the values Tg are situated above additive glass transition temperature, for CP-OFD-lO/P-1 — lower and for diblock-copolymers CP-OFD-lO/OSF-10 the dependence Tg(cform) has sigmoid character. Such course of the dependences Tg(cform) for the indicated copolymers supposes different change Kh with copolymers composition. The value KM can be estimated according to tlie well-known Gordon-Talor-Wood equation [143] ... 

The glass transition temperatures of copolymers with high content of NVK deviate from Flory-Fox or Gordon-Tailor equations, but they fit the Johnston equation. 

FIGURE 21 Glass transition temperature versus weight fractions of PEO for PEO/ PnBMA blends. The solid and dotted line represent theoretical T-composition curves according to Fox and Gordon-Taylor equations, respectively. Modified from Mandal et al., (2000). 

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. 

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 description of the historic Gordon-T ay lor and Wood equations for the glass transition of solutions and copolymers can be found in Gordon M, Taylor IS (1952) Ideal Copolymers and the Second-order Transitions of Synthetic Rubbers. I. Noncrystalline Copolymers. J Appl Chem 2 493-500 Wood LA (1958) Glass Transition Temperatures of Copolymers. 1 Polymer Sci 28 319-330 for the relationship to the volume changes, see Kovacs AJ (1964) Glass Transition in Amorphous Polymers. Phenomenological Study. Fortschr Hochpolym Forsch 3 394-508. 

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