Theory of melting in multicomponent systems of polymers

A theory is developed for the equilibrium crystalline state and melting in multicomponent systems of crystallizable polymers (species μ) and solvents (species m) by extending the Flory theory for binary systems of a single polymer and a solvent. Relationships deduced from the free energy of fusion for multicomponent systems are examined. The formula for the equilibrium crystallite length ζα for μ=α is common for all polymer components μ. The relationship of melting temperature Tm(α) for μ=α involves the degree of crystallinity (1−λμ) for all μ and interaction parameters of all polymer–polymer, polymer–solvent, and solvent–solvent contacts, i.e., χμν, χμm, and χmn. The degree of crystallinity (1−λα) for each component μ=α can be obtained by solving the simultaneous equations of melting temperatures Tm(μ) for the components μ which are coexistent in the crystalline state under a given condition of the system. The theory is applied to systems involving two crystallizable polymer components and the features of melting temperature diagram predicted from the theory are examined.