Extension of the FH Theory to Crystal-Amorphous Blends

Polymer crystallization has been described in the framework of a phase field free energy pertaining to a crystal order parameter in which = 0 defines the melt and assumes finite values close to unity in the metastable crystal phase, but = 1 at the equilibrium limit (23-25). The crystal phase order parameter (xj/) may be defined as the ratio of the lamellar thickness (f) to the lamellar thickness of a perfect polymer crystal (P), i.e., xlr = l/P, and thus it represents the linear crystallinity, that is, the crystallinity in one dimension. The free energy density of a polymer blend containing one crystalline component may be expressed as 

The free energy density of the crystal solidification may be expressed in the context of the asymmetric Landau expansion,/(i/f) as 

The establishment of phase diagrams using the phase field model of crystallization is accomplished by minimizing the free energy of the mixture with respect to the nonconserved order parameters and finding the minimum free energy of the mixture at each composition. We then minimize/(yf, (p) with respect to ip- in order to find the roots, leading to 

For the neat crystal, that is, 0 = 1, the lower right-hand side of equation 16.6 becomes zero, thus ip = signifies the unstable potential hump, and = fg 

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