Equations couchman-karasz

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]. 

Figure 19. Tg values determined by DSC, DMT A, DRS, and TSEXD versus LPU content. The dotted line is a fit of Fox s equation (eq. 2) to the DMTA data and the dashed line is a fit of the Couchman-Karasz equation (eq. 3) to the DSC data.

Figure 9 shows the concentration dependences of obtained from the predictions based on Fox and Couchman-Karasz equations. 

This can be seen to be equivalent to the Couchman-Karasz equation where k is equal to the ratio of the specific heats instead of pi Aa2/P2Aai as in the original paper [11]. P and Aa are the density and thermal expansivity respectively ... 

The Ten Brinke modification of the Couchman-Karasz equation was proposed to describe the lowering of the glass transition temperature of a cross-hnked polymer network by a low molecular weight diluent [12]. 

These curves are well described by equations such as the Gordon-Taylor, the Couchman-Karasz and modifications thereof (see Section 1.5.8), with water taking the role of plasticiser. 

FIGURE 13.1 Experimental T values resulting from the antiplasticization effect of PVP90 (o), PVP12 (o), or MD simulated values for PVP (>t) in amorphous mixtures with indomethacin. r predicted is based on the Gordon-Taylor equation with the value of K estimated using the Couchman and Karasz relationship. 

One of the properties that is affected by the production of miscible blends is the glass transition temperature or Tg. The Tg of miscible blends has been modeled using several different approaches in the literature (Wood 1958 Couchman and Karasz 1978). The simplest of these is the Flory-Fox equation ... 

Figure 11.6 Schematic representation of relationships between water activity, water content, Tg and viscosity for wheat gluten-based films. Calculated values were obtained using the (GAB) equation [176], Couchman and Karasz equation (CK) [171], and Williams Landel and Ferry equation (WLF) [153]. The critical water activity (aw) and Me are indicated when Tg is equal to the ambient temperature...

The empirical DiBenedetto equation was developed in the late 1960s to mathematically relate Tg and conversion (Nielson 1969 DiBenedetto 1987). Excellent theoretical treatises on the Tg-conversion relationship can be found in Pascault and Williams (1990), Hale et al. (1991), and Venditti and Gillham (1997). Venditti and Gillham (1997) developed an equation based on thermodynamic considerations put forth by Couchman and Karasz (1978) to predict Tg versus mole fraction of constituents of a linear copolymer ... 

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