Bueche equation

PTT exhibits melt rheological behavior similar to that of PET. At low shear rates the melt is nearly Newtonian. It shear-thins when the shear rate is >1000s 1 (Figure 11.10) [68], At the melt processing temperatures of PET, 290°C, and of PTT, 260°C, both polymers have similar viscosities of about 200Pas. However, PTT has a lower non-Newtonian index than PET at high shear rates. The flow behavior can be modeled by the Bueche equation, as follows ... 

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 Cahn theory of spinodal decomposition explains the essential features of phase transition in the unstable region. The scale of phase separation was predicted and exceeded by an order of magnitude the scale in low molecular weight systems. A comparison of the diffusion coefficient estimated by the rate of spinodal decomposition agrees with the value predicted by the Bueche equation. The high level of phase interconnectivity predicted by the Cahn theory was also observed experimentally. 

This is the three dimensional form of the Debye-Bueche equation which may be used to describe the scattering of oriented systems. For samples... 

Equation 4.130 is the usual form of the Debye-Bueche equation. This equation generally describes the scattering from a spherically symmetrical system provided a suitable expression can be found for the correlation function. For many systems, an exponential correlation... 

The Debye-Bueche equation is more general than just for light scattering and applies also to x-ray and neutron scattering, but in these cases, the p s and the K s will be different. 

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-... 

Equations for Tg based on the free-volume concept have been proposed for miscible polymer blends and they are similar to the Kelly-Bueche equation given above for polymer-diluent systems. Likewise, this description in terms of a single Tg over-simplifies the dynamics of the components in the blend and neglects some important elements. An important element for interpreting the relaxation behavior of blends is fluctuations in concentration or composition [102]. Models have been... 

In the second stage, we assume that the correlation between the neighboring domains increases. We assume the correlation function y(r) is y r) = exp(-r/( following Debye and Bueche [71], where is the averaged electron density. Substituting this y(r) into Equation (5.32) gives the Debye-Bueche equation ... 

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