Skip to main content

Description of polymer solutions phase equilibria by cubic equation of state with different mixing rules


In this paper, experimental data available in the literature are used to test the Peng-Robinson (PR) equation of state for representing VLE of concentrated polymer solutions in conventional solvents. The most important issues of extending cubic EoS to polymers are the description of the pure component EoS parameters, a and b, for polymers and selection of mixing rules. To capture nonidealities, several existing mixing rules are adopted, namely, vdW1, vdW2, Wong-Sandler, and Zhong and Masuoka. The A E term in the Wong-Sandler mixing rule is evaluated by the Flory-Huggins model. Therefore, the experimental data are calculated by the PR equation of state incorporating different mixing rules, including the consideration of binary interaction parameters and liquid phase parameters. After determining the binary interaction parameter k ij , the Flory interaction parameter χ, and the number of solvent-size segments parameter r, using experimental vapor-liquid equilibria data, it was possible to obtain excellent correlations of the VLE data for these systems. The Wong-Sandler rule seems to give better results in representing the properties of polymeric solutions. This can be explained by the size difference between the polymer and the solvent, which means that one parameter is not sufficient to describe this disparity.

This is a preview of subscription content, access via your institution.


  1. 1.

    Xiong, Y. and Kiran, E., Polymer, 1994, vol. 35, p. 4408.

  2. 2.

    Kontogeorgis, M.G., Fredenslund, A., Economou, I.G., and Tassios, D.P., AIChE J., 1994, vol. 40, p. 1711.

  3. 3.

    Kalospiros, N.S. and Tassios, D.P., Ind. Eng. Chem. Res., 1995, vol. 34, p. 2117.

    Article  Google Scholar 

  4. 4.

    Zhong, C. and Masuoka, H., Fluid Phase Equil., 1996, vol. 123, p. 59.

  5. 5.

    Bertucco, A. and Mio, C., Fluid Phase Equil., 1996, vol. 117, nos. 1/2, p. 18.

    Article  Google Scholar 

  6. 6.

    Orbey, N. and Sandler, S.I., AIChE J., 1994, vol. 40, p. 1203.

    Article  Google Scholar 

  7. 7.

    Rodgers, P.A., J. Appl. Polymer Sci., 1993, vol. 48, no. 6, p. 1061.

    Article  Google Scholar 

  8. 8.

    Zhong, C. and Masuoka, H., Fluid Phase Equil., 1998, vol. 144, nos. 1/2, p. 49.

    Article  Google Scholar 

  9. 9.

    Daubert, T.E. and Danner, R.P., Physical and Thermodynamic Properties of Pure Compounds: Data Compilation, New York: Hemisphere Publ., 1990.

    Google Scholar 

  10. 10.

    Magoulas, K. and Tassios, D., Fluid Phase Equil., 1990, vol. 56, p. 119.

    Article  Google Scholar 

  11. 11.

    Mathias, P.M. and Copeman, T.W., Fluid Phase Equil., 1983, vol. 13, p. 91.

    Article  Google Scholar 

  12. 12.

    Rasmussen, P., Holten-Andersen, J., and Fredenslund, A., Ind. Eng. Chem. Res., 1987, vol. 26, p. 1382.

    Article  Google Scholar 

  13. 13.

    Wong, D.S. and Sandler, S.I., AIChE J., 1992, vol. 38, p. 671.

    Article  Google Scholar 

  14. 14.

    Bawn, C.E. and Wajid, M.A., Trans. Faraday Soc., 1956, vol. 52, p. 1658.

    Article  Google Scholar 

  15. 15.

    Eichinger, B.E. and Flory, P.J., Macromolecules, 1968, vol. 5, p. 1285.

    Google Scholar 

  16. 16.

    Flory, P.J. and Hoecker, H., Trans. Faraday Soc., 1971, vol. 67, no. 8, p. 2258.

    Article  Google Scholar 

  17. 17.

    Booth, C. and Devoy, C.J., Polymer, 1971, vol. 12, no. 5, p. 311.

    Google Scholar 

  18. 18.

    Wen, H., Elbro, H.S., and Alessi, P., Polymer Solution Data Collection Part I: Vapor-Liquid Equilibrium, DECHEMA Chem. Data Ser., Frankfurt: DECHEMA, 1991.

    Google Scholar 

  19. 19.

    Bawn, C.E., Freeman, R.F., and Kamaliddin, A.R., Trans. Faraday Soc., 1950, vol. 46, p. 677.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Mehdi Baniasadi.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Baniasadi, M., Baniasadi, M. & Ghader, S. Description of polymer solutions phase equilibria by cubic equation of state with different mixing rules. J. Engin. Thermophys. 20, 115–127 (2011).

Download citation


  • Bubble Point Pressure
  • Binary Interaction Parameter
  • Engineering THERMOPHYSICS
  • Concentrate Polymer Solution