Kelley-Bueche equation

Such behaviour, with a continuously decreasing slope, is not always found. There are many examples where two descending curves that come together in a cusp (Braun and Kovacs, 1965). Results by Pezzin et al. (1968,1971) are shown in Fig. 16.6 for PVC in two plasticizers. For this kind of behaviour results can be fitted with two equations one above and the other below the temperature Tc of the cusp. For temperatures above Tc use can be made of the Kelley-Bueche equation (1961) ... 

Keesom forces, 242 Kelley-Bueche equation, 611 Kerr effect, 299, 349 Kinetic(s)... 

The impression of a simple relationship given by Fig. 12.7 is misleading since a continuously decreasing negative slope is indicated. For polystyrene, PS, solutions in toluene [58] and OT-tricresyl phosphate [59,60] this has been shown not to be the case. In 1964 Braun and Kovacs reported results on the polystyrene/toluene system which showed two descending curves which came together in a cusp [58] (see Fig. 12.8). The results were rationalized by fitting the Kelley-Bueche equation [61],... 

Often the TgS of miscible (or partially miscible) blends are compared with values calculated from the Kelley-Bueche equation (Eq. 21) [55]. which is based on the additivity of free and occupied volumes of the individual components, the Gordon-Taylor equation (Eq. 22) [56] or the Fox equation (Eq. 23) [57] for a binary mixture of A and B is the glass-transition temperature of the mixture, (l>A> g,A> g,B volume and weight fractions and glass-tran-... 

A logarithmic form of this equation is given by Pochan et al. Other expressions include the Wood equation the Kelley-Bueche expression the Gordon-Taylor equation and the DiMarzio-Gibbs equation None of these Equations directly take into account the specific interactions within a blend. 

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 ... 

Figure 5-6. (a) Dependence of T on p for mixtures of polymethyl methacrylate with diethyl phthalate. Comparison of experimental results with equation (5-8). Parameters found were ctjctp = 2.32, Tgd = -57 °C, Tgp = 104 °C.f [After F. N. Kelley and F. Bueche, J. Polym. Sci., 50 549 (1961)] (b) Variation of Tg for a miscible polymer blend of polycaprolactone (PCL) and poly(styrene-co-acrylonitrile) (SAN), with a description of the data using the Gordon-Taylor relationship, equation (5-27). The two points at low SAN content have a higher-than-expected Tg because of crystallization of the PCL. [After S-C. Chiu and T. G. Smith, J. Appl. Polym. Sci., 29,1797 (1984). Copyright 1984, Wiley Periodicals, Inc., a Wiley Company.]... 

Kelley and Bueche " derived similar equations for the composition dependence of polymer-diluent systems from free-volume considerations and also showed acceptable fits to the data. The parameters used to fit equation (63) to the data are generally found to be in the range expected from free-volume arguments. Of particular interest is the fact that at small diluent-contents, one finds that equation (61) corresponds to ... 

---