Phase Behavior of
Ternary Polymer Mixtures
Part 3

Most products made of polymers are blends of more than two components and, in many cases, more than one polymer. The thermodynamics of these polymer blends can be described with the compressible regular solution free energy model of Ruzette and Mayes (2001)1,2. This model makes only use of pure component properties which are assumed to be concentration and temperature dependent, that is, the model avoids the direct calculation of the temperature and concentration dependency of the Flory-Huggins interaction parameter.
Once all pure component properties have been calculated, the ternary phase curves for weakly interacting polymer systems can be easily calculated. The spinodal points which define the boundary between the stable and metastable regions are usually sufficient to qualitatively describe the phase behavior of ternary systems. Following Scott3, the stability criterion for spinodal points of ternary systems are found by solving following equation:

Scott's spinodal condition has the following solutions:

where ρr,i = ρi / ρhc,i = vi / vhc,i is the reduced density4, δ0,i2 = ρr,i, δi2 is the corresponding hardcore cohesive energy density, and φ1 and φ2 are the volume fractions of the two components,

φi = Ni ri vi / Σ(Nj rj vj )

The compressible regular solution model presented here is only applicable to weakly interacting systems. As Gonzales and Ruzette have shown2, the agreement with the experimental data for those sytems is quite good, despite the many simplifying assumptions of the model.


  1. Anne-Valerie G. Ruzette and Anne M. Mayes, Macromolecules 34, 1894-1907 (2001)

  2. Juan A. Gonzalez-Leon and Anne M. Mayes, Macromolecules 36, 2508-2515 (2003)

  3. R. L. Scott, J. Chem. Phys. 17, 268 (1949)
  4. The hard core volume is the volume of a repeat unit at zero Kelvin and zero pressure. Most investigators assume that vhc is equal to the closed packed volume of the molecules at zero Kelvin.


  • Summary


    The thermodynamics of ternary polymer blends can be described with the compressible regular solution free energy model of Ruzette and Mayes.

  • This model captures the phase behavior of weakly interacting polymer pairs using only the pure component properties of mass density, solubility parameter, and thermal expansion coefficient.

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