Homogeneous melt background

The first class of blends to be analyzed is that of a homogeneous, disordered liquid phase in equilibrium with a pure crystalline phase, or phases. If both species crystallize they do so independently of one another, i.e. co-crystallization does not occur. With these stipulations the analysis is relatively straightforward. The chemical potentials of the components in the melt are obtained from one of the standard thermodynamic expressions for polymer mixtures. Either the Flory-Huggins mixing expression (7) or one of the equation of state formulations that are available can be used.(8-16) The melting temperature-composition relations are obtained by invoking the equilibrium requirement between the melt and the pure crystalline phases. When nonequilibrium systems are analyzed, additional corrections will have to be made for the contributions of structural and morphological factors. 

The melting temperature-composition relation for the conunon situation of two dissimilar polymers, only one of which crystallizes, was formulated by Nishi and Wang.(17) This relation is based on the free energy of mixing of two dissimilar polymers in the disordered state, as given by Scott (18), within the framework of the Flory-Huggins lattice treatment.(7) The chemical potentials of each species in the binary mixture can be expressed as 

Let species 2 be designated as the crystallizing component. Dividing Eq. (4.2) by the number of structural repeating units per molecule (Vo/V2u)X2y where V2u is the volume of the repeating unit, the chemical potential per repeating unit, /T2u becomes 

Equation (4.4) can be compared with the analogous equation given by Nishi and Wang(17) 

Using Eq. (3.7), the expression for the chemical potential of a unit in the crystal relative to that in the melt, along with Eq. (4.5), the equilibrium condition yields 

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