Kwei equation

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]. 

L. L. Blyler and T. K. Kwei [39] proposed the direct opposite (to 4). In their reasoning, they proceeded from the known and generally acceptable Doolittle equation, which puts liquid viscosity in exponential dependence on the inverse value of the free volume of the latter. According to [39], gas has a volume of its own, the value of which it contributes to the free volume of the polymer when it dissolves therein as a result, viscosity falls. The theoretical formula obtained by the authors was experimentally confirmed in the same work. The authors measured pressure values at the entrance of cylindrical capillaries, through which melts of both pure polyethylene, and polyethylene with gas dissolved in it, extruded at a constant rate. 

A modified version of this equation has been used by some other authors [Kwei and Frisch., 1978 Walsh et al, 1985], who added a constant that is related to the morphology of the crystalline region ... 

An equation has been proposed by Kwei that attempts to address this ... 

Still another approach to predicting the thermal expansion coefficient of composites has been taken by Wang and Kwei (1969), who derived expressions to account for deviations from a simple additivity rule due to the development of thermal stresses. Such stresses will arise in practice if a composite is cooled from its fabrication temperature and if the components have different coefficients of expansion. They obtained the following equations to give the linear coefficient of expansion of the composite 5 ... 

Figure 12.35. Comparison of experimental values of linear coefficient of expansion of a Ti02-filled epoxy resin with values predicted by equation (12.54). The dashed curve is for the rule of mixture, the solid curve for the predictions of equation (12.54). Temperature range -50 C to 100°C df = 1 x 10" °C Ef = 7.25 x lO psi Vf = 0.23 dip = 55 X lO" C = 7.25 x 10 psi = 0.3. (Wang and Kwei,...

One of the most comprehensive comparisons of data for many filled polymer systems is given in the review by Holliday and Robinson (1973), which also provides additional expressions not discussed here. Several points are of special interest. First, equations such as Kerner s (1956a,h) and Wang and Kwei s (1969) agree reasonably well for spherical particles, while Turner s (1946) equation is better for systems in which fillers are fibrous or platelike. Second, fibers and fabrics induce the greatest deviation from additivity (see Figure 12.36). Finally, the behavior of polytetrafluoro-ethylene is strikingly anomalous. 

Chemical reactions (32.7), (32.9), and (32.10) are exothermic, whereas steam reforming [Eq. (32.8)] is endothermic, which means that heat must be supplied. Equation (32.7) requires Imol of methane to form 2 mol of hydrogen. For the considered 10 kWei system, about 0.0406 mol s" of methane is necessary. Taking the LHV of methane into account, that is, 802.15 kj mol h an enthalpy flow of 32.6 kWth (LHV CH4) can be determined, leading to a gross efficiency of 30.7% based on Eq. (32.11) ... 

From the NMR study of Kwei and coworkers [4] it appears reasonable to assume that the volume fraction of each phase remains constant and equal to the equilibrium value at all times. From the M versus PS plots, such as shown in Figure 8, together with Equations (14-16), it is possible to relate Iq/Im phase separated blend to a unique value of the rich phase composition... 

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