Phase Diagrams of Binary Crystalline−Crystalline Polymer Blends

Abstract

A thermodynamically self-consistent theory has been developed to establish binary phase diagrams for two-crystalline polymer blends by taking into consideration all interactions including amorphous-amorphous, crystal-amorphous, amorphous-crystal, and crystal-crystal interactions. The present theory basically involves combination of the Flory-Huggins free energy for amorphous-amorphous isotropic mixing and the Landau free energy of polymer solidification (e.g., crystallization) of the crystalline constituents. The self-consistent solution via minimization of the free energy of the mixture affords determination of eutectic, peritectic, and azeotrope phase diagrams involving various coexistence regions such as liquid-liquid, liquid-solid, and solid-solid coexistence regions bound by liquidus and solidus lines. To validate the present theory, the predicted eutectic phase diagrams have been compared with the reported experimental binary phase diagrams of blends such as polyethylene fractions as well as polycaprolactone/trioxane mixtures.

Phase Field Modeling on Polymer Crystallization and Phase Separation in Crystalline Polymer Blends

“…More importantly, the crystalline-solvent phase diagrams, thus solved in the context of the Flory-Huggins theory alone, cannot account for the existence of the solidus line, because the crystal phase always coincides with the pure crystalline polymer axis due to the inherent assumption, adopted from Prigogine theory, of the complete rejection of solvent molecules from the crystalline phase [66,67]. Thus, the binary phase diagrams of crystalline polymer blends are at odds with those of the small molecule systems including organic compounds [60], metal alloys [68], ceramic glasses [69], and liquid crystal mixtures [70].…”

“…Matkar have hypothesized what would happen to crystalline blend phase diagrams if one relaxes the last assumption of the Flory diluent theory of crystalline polymer solutions, namely, the complete rejection of polymeric solvent from the crystalline phase [66,67]. In addition, Xu have developed a new theory for a binary crystalline polymer blends based on a combination of liquid-liquid phase separation and solid-liquid phase transition by taking into consideration the cou pling interaction between the solid crystal and amorphous liquid phase [71].…”

Discrepancy in determination of χ parameters by melting point depression versus small-angle neutron scattering in blends of deuterated polycarbonate and isotactic poly(methyl methacrylate)

“…A unified theoretical model (Matkar & Kyu, 2006b) has been developed in the framework of the phase field model of solidification involving the Landau-type double-well potential pertaining to the first order solid-liquid phase transition (Xu et al, 2005) coupled with the FH free energy for liquid-liquid demixing (Flory, 1953).…”

“…ac ð 2 2 Þð 1 2 Þ, representing the amorphous-crystal interaction. By the same token, the cross-interaction term, cc ð 1 1 Þð 2 2 Þ, may be interpreted as the crystal-crystal interaction of the co-crystals (Matkar & Kyu, 2006b). …”

“…These anisotropic interactions of separate crystals and co-crystals are complimentary to aa , representing the isotropic interaction of amorphous materials. Moreover, these crystal-amorphous interaction parameters may be estimated from the heat of fusions of the crystals, i.e., ca / W 1 ¼ 6ðÁH Furthermore, the crystal-crystal interaction may be expressed as a geometric mean of the crystal-amorphous and amorphous-crystal interactions to account for the non-ideal rule of the crystalline mixture, i.e., cc ¼ c w ½ð ca Þ 1=2 ð ac Þ 1=2 , in which c w represents the anisotropic interaction parameter, which signifies any departure from ideality (Matkar & Kyu, 2006b).In the present case, PC and iPMMA show no indication of cocrystallization, thus c w may be taken as zero or negligibly small, i.e. 0.001 in the present case.…”