Gordon-Taylor relation

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. 

Butyllithium-initiated homopolymerisation of butadiene results in a BR polymer containing random distributed cis-1,4, trans-1,4 and 1,2-BR or vinyl-BR units. The concentration of the catalyst modifier and the polymerisation temperature (between 40°C and 75°C) determine the concentrations of the three different components. Thus, BR rubber is in fact nearly always a terpolymer and its Tg-value can be described by means of the Gordon-Taylor relation [7]. This relation is written in its general form as ... 

A few experimental data were available based on SSBR (Tg-value = 197 K, three systems) and on ESBR (Tg-value = 215 K, two systems) both extended with an aromatic oil. The Tg-value of the rubber phase is in both cases lower than that of the oil phase i.e. the SSBR/ESBR rubber phases are for Tg-rubber < temperatures < Tg-oil, filled with glassy oil particles, resulting in an increased Tg-value of the rubber after the oil addition. The experimental values could be fitted again satisfactorily using the Gordon-Taylor relations ... 

One experimental value was available for a SSBR sample (Tg-value = 232 K) extended with a naphtenic (Tg-value = 208 K). The Tg-value of the rubber phase is now higher than that of the oil phase i.e. the oil will act as a plasticiser in the temperature region between Tg-oil and Tg-rubber and the Tg-value of the rubber is decreased after the oil addition. Assuming that also in this case the experimental values are described by the Gordon-Taylor relation, the equation might hold ... 

All these commercially produced BR systems are amorphous rubbers under atmospheric conditions. The Tg-value of these systems, depending on their structure, is described by the Gordon-Taylor relation, see Chapter 1. BR becomes a semicrystalline polymer under atmospheric conditions if the 1,4 trans-BR content is higher than about 70 %wt. or if a syndio-or isotactic 1,2-BR phase is present. This is shown by the results of thermo-analytical measurements on experimental BR systems with a high trans content and with a high syndiotactic 1,2-BR content which are reported in this chapter. Moreover, the Tg-values of two series of IR samples containing 1,2- and 3,4-IR are used to determine the Tg/structure relation for non-polar polymers with side-chains. 

The effects of copolymerization vary from one system to another but a large number of copolymer rubbers obey the Gordon-Taylor relation quite closely. In effect this proposes that the T, of a copolymer can be linearly interpolated from the TgS of the appropriate homopolymers. Butadiene-styrene random copolymers provide a very good fit but in general interactions between the... 

There are several equations to describe Tg-composition dependence in miscible blends, for example the Gordon-Taylor, Fox, Kelley-Bueche or Kanig equations [60-63] however, there are systems that do not fit to any of them. The Gordon—Taylor equation may serve here as an example of the relations mentioned above ... 

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]. 

On notera que cette relation ne fait pas intervenir I hypothese d invariance du volume libre it T . Cette hypothese restrictive (/ea = fg>2 = /ffi C) ne constitue, en effet, qu un cas particulier de l eq. (124). L expression (125) est par ailleurs sensiblement identique celles de Gordon et Taylor (1952), de Mandelkern et al. (1957), et de Kelley et Bueche (1961). TgtX represente une moyenne ponderee (par le rapport des coefficients A et A eta) entre Tffil et T tS. 

Crank, J. The Mathematics of Diffusion, 2nd Ed., Clarendon Press, Oxford, 1975. Gordon, M. and Taylor, J.S. Ideal copolymers and second order transitions in synthetic rubbers. I. Non-crystalline polymers, /. Appl. Chem., 2, 493,1952. Karel, M., Anglea, S., Buera, M.P., Karmas, R., Levi, G., Roos, Y. et al. Stability related transitions of amorphous foods, 246. pp. 249,1994. 

Nieuwenhuijsen MJ, Putcha V, Gordon S, Heederik D, Venables KM, Cullinan P, Newman-Taylor AJ. Exposure-response relations among laboratory animal workers exposed to rats. Occup Environ Med 2003 60 104-108. 

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. 

Cullinan, R, D. Lowson, M. J. Nieuwenhuijsen, S. Gordon, R. D. Tee, K. M. Venables, J. C. McDonald, and A. J. Newman Taylor. 1994. Work-related symptoms sensitization and estimated exposure in workers not previously exposed to laboratory rats. Occupational and Environmental Medicine 51 589-592. 

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