Miscibility maps for polymer blends: Effects of temperature, pressure, and molecular weight

• Published in: Journal of polymer science. Part B, Polymer physics Vol. 52; no. 6; pp. 419 - 443
• Main Authors: Masnada, Elian M., Julien, Grégoire, Long, Didier R.
• Format: Journal Article
• Language: English
• Published: Hoboken, NJ Blackwell Publishing Ltd 15.03.2014; Wiley; Wiley Subscription Services, Inc
• Subjects: Applied sciences; Behavior; blends; Exact sciences and technology; Exact solutions; Mathematical models; Miscibility; Molecular weight; Organic polymers; phase behavior; phase separation; Phase transformations; Physicochemistry of polymers; Polymer blends; Polymerization; Properties and characterization; Temperature; theory; Thermal and thermodynamic properties; thermodynamics; PVT diagram; Mean field approximation; Polymer blends; Phase diagram; Theoretical study; thermodynamics; Modeling; phase behavior; phase separation; miscibility; Thermodynamic model; blends; theory
• ISSN: 0887-6266; 1099-0488
• DOI: 10.1002/polb.23436

ABSTRACT We study a Gibbs free energy model for describing the thermodynamics of compressible polymer blends in the case of nonpolar polymers. This model is a mean field model equivalent to the cell model of Prigogine et al. and close also to the model by Flory‐Orvoll and Vrij. The model is expressed as a function of the interaction energies between monomer pairs (a, b, and c), the degrees of polymerization (XA and XB), a close packing parameter ρ0, the temperature, and the pressure. We derive an analytical expression regarding blend miscibility. All the already observed phase behaviors are recovered: the occurrence of two kinds of upper critical solution transition (UCST): case‐I and case‐II UCST for which the pressure has a destabilizing or stabilizing effect, respectively, and lower critical solution transition; cases where the pressure have a non‐monotonous effect on the UCST temperature; cases where the spinodal lines close up under high pressures; and the so‐called hour‐glass transition. The model allows for making explicit the effect of the different physical parameters on phase behavior. We calculate complete miscibility maps regarding the occurrence of the various possible kinds of transitions in the 2D space b/a and XA, for different values of (c−ab)/a, applied pressure P, and chain length ratios. This approach may come as a complement to already existing, more quantitative and elaborated approaches. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014, 52, 419–443 Polymer blends exhibit complex phase behaviors with various kinds of phase transitions: lower critical solution transitions, case‐I upper critical solution transitions, case‐II upper critical solution transitions, or hour‐glass‐like phase diagrams. The pressure may have a stabilizing effect or a destabilizing one. Miscibility maps regarding the occurrence of the various kinds of phase transitions, as a function of the difference in the self‐energies of the constituents and of their molecular weights, are calculated for different molecular weight ratios.