Prediction of Henry's Constant in Polymer Solutions using the Peng-Robinson Equation of State
The peng-Robinson (PR), a cubic equation of state (EoS), is extended to polymers by using a single set of energy (A1, A2, A3) and co-volume (b) parameters per polymer fitted to experimental volume data. Excellent results for the volumetric behavior of the 11 polymer up to 2000 bar pressure are obtained. The EoS is applied to the correlation and prediction of Henry constants in polymer solutions comprising three polymer and many nonpolar and polar solvents, including supercritical gases. The correlation achieved with two adjustable parameter is satisfactory compared with the experimental data. As a result, the present work provides a simple and useful model for the prediction of Henry's constant for polymer containing systems including those containing polar, nonpolar and supercritical fluids.
[1] Flory, P. J., Principles of Polymer Chemistry, Ithaca, NY, Cornell
University Press (1953).
[2] Oishi, T. and J. M. Prausnitz, "Estimation of solvent activities in polymer
solutions using a group-contribution method," Industrial & Engineering
Chemistry, Process Design and Development, 17, 333-339 (1978).
[3] Elbro, H. S., A. Fredenslund and P. Rasmussen, "A new simple equation
for the prediction of solvent activities in polymer solutions," Macromolecules,
23, 4707- 4714 (1990).
[4] Bondi, A., Physical Properties of Molecular Crystals, Liquids, and Glasses,
New York, John Wiley & Sons (1968).
[5] Radfarnia, H. R., G. M. Kontogeorgis, C. Ghotbi and V. Taghikhani,
"Classical and recent free-volume models for polymer solutions: A
comparative evaluation,"Fluid Phase Equilibria, 257, 63-69 (2007).
[6] Zhong, C., Y. Sato, H. Masuoka and X. Chen, "Improvement of predictive
accuracy of the UNIFAC model for vapor-liquid equilibria of polymer
solutions," Fluid Phase Equilibria, 123, 97-106 (1996).
[7] Morris, W. O., P. Vimalchand and M. D. Donohue, "Perturbed-soft-chain
theory: An equation of state based on the Lennard-Jones potential," Fluid
Phase Equilibria, 32, 103-115 (1987).
[8] High, M. S. and R. P. Danner, "Application of the group contribution
lattice-fluid equation of state to polymer solutions," AIChE Journal, 36, 1625-
1632 (1990).
[9] Chen, F., A. Fredenslund and P. Rasmussen, "Group-contribution Flory
equation of state for vapor-liquid equilibria in mixtures with polymers,"
Industrial & Engineering Chemistry Research, 29, 875-882 (1990).
[10] Akbarzadeh ,K., M.Moshfeghian, "Application of the polymer chain-ofrotator
(PCOR) equation of state and its extension to polymer blends", Fluid
Phase Equilibria 187-188 , 347361 (2001) .
[11] Harismiadis, V. I., G. M. Kontogeorgis, A. Fredenslund and D. P.
Tassios, "Application of the van der Waals equation of state to polymers II.
Prediction" ,Fluid Phase Equilibria, 96, 93-117 (1994).
[12] Peng, D. and D. B. Robinson, "New two-constant equation of state,"
Industrial & Engineering Chemistry Fundamentals, 15(1), 59-64 (1976).
[13] Androulakis, I.P., N.S. Kalospiros, and D.P. Tassios, Thermophysical
properties of pure polar and nonpolar compounds with a modified VdW-711
equation of state, Fluid Phase Equil., 45, 135-163 (1989).
[14] Louli, V. and D. Tassios, "Vapor-liquid equilibrium in polymer-solvent
systems with a cubic equation of state," Fluid Phase Equilibria, 168, 165-182
(2000).
[15] Kontogeorgis, G. M., A. Fredenslund and D. P. Tassios, "Simple activity
coefficient model for the prediction of solvent activities in polymer solutions,"
Industrial and Engineering Chemistry Research, 32, 362-372 (1993).
[16] Patrick A. Rodgers,"Pressure-volume-temperature relationships for
polymeric liquids: A review of equations of state and their characteristic
parameters for 56 polymers", Journal of Applied Polymer Science, 48, 1061-
1079(1993).
[17] Zhong , C. and H. Masuoka," Prediction of Henry's constants for
polymer-containing systems using the SRK equation of state coupled with a
new modified UNIFAC model ",Fluid Phase Equilibria,126,1-12(1996).
[18] Maloney, D. and J. Prausnitz,"Solubility of ethylene and other organic
solutes in liquid, low density polyethylene in the region 124 o to 300 o c",
AIChE Journal, 22,74-82(1976).
[19] Leonard , I. and D. Harnish, "Solubility of gases and liquids in molten
polystyrene", AIChE journal, 22, 117-121(1976).
[20] Liu, D. M. Prausnits,"Solubilities of volatile solutes in poly vinyl acetate
from 125 to 200oC", Journal of polymer science, 15, 145-153(1977).
[1] Flory, P. J., Principles of Polymer Chemistry, Ithaca, NY, Cornell
University Press (1953).
[2] Oishi, T. and J. M. Prausnitz, "Estimation of solvent activities in polymer
solutions using a group-contribution method," Industrial & Engineering
Chemistry, Process Design and Development, 17, 333-339 (1978).
[3] Elbro, H. S., A. Fredenslund and P. Rasmussen, "A new simple equation
for the prediction of solvent activities in polymer solutions," Macromolecules,
23, 4707- 4714 (1990).
[4] Bondi, A., Physical Properties of Molecular Crystals, Liquids, and Glasses,
New York, John Wiley & Sons (1968).
[5] Radfarnia, H. R., G. M. Kontogeorgis, C. Ghotbi and V. Taghikhani,
"Classical and recent free-volume models for polymer solutions: A
comparative evaluation,"Fluid Phase Equilibria, 257, 63-69 (2007).
[6] Zhong, C., Y. Sato, H. Masuoka and X. Chen, "Improvement of predictive
accuracy of the UNIFAC model for vapor-liquid equilibria of polymer
solutions," Fluid Phase Equilibria, 123, 97-106 (1996).
[7] Morris, W. O., P. Vimalchand and M. D. Donohue, "Perturbed-soft-chain
theory: An equation of state based on the Lennard-Jones potential," Fluid
Phase Equilibria, 32, 103-115 (1987).
[8] High, M. S. and R. P. Danner, "Application of the group contribution
lattice-fluid equation of state to polymer solutions," AIChE Journal, 36, 1625-
1632 (1990).
[9] Chen, F., A. Fredenslund and P. Rasmussen, "Group-contribution Flory
equation of state for vapor-liquid equilibria in mixtures with polymers,"
Industrial & Engineering Chemistry Research, 29, 875-882 (1990).
[10] Akbarzadeh ,K., M.Moshfeghian, "Application of the polymer chain-ofrotator
(PCOR) equation of state and its extension to polymer blends", Fluid
Phase Equilibria 187-188 , 347361 (2001) .
[11] Harismiadis, V. I., G. M. Kontogeorgis, A. Fredenslund and D. P.
Tassios, "Application of the van der Waals equation of state to polymers II.
Prediction" ,Fluid Phase Equilibria, 96, 93-117 (1994).
[12] Peng, D. and D. B. Robinson, "New two-constant equation of state,"
Industrial & Engineering Chemistry Fundamentals, 15(1), 59-64 (1976).
[13] Androulakis, I.P., N.S. Kalospiros, and D.P. Tassios, Thermophysical
properties of pure polar and nonpolar compounds with a modified VdW-711
equation of state, Fluid Phase Equil., 45, 135-163 (1989).
[14] Louli, V. and D. Tassios, "Vapor-liquid equilibrium in polymer-solvent
systems with a cubic equation of state," Fluid Phase Equilibria, 168, 165-182
(2000).
[15] Kontogeorgis, G. M., A. Fredenslund and D. P. Tassios, "Simple activity
coefficient model for the prediction of solvent activities in polymer solutions,"
Industrial and Engineering Chemistry Research, 32, 362-372 (1993).
[16] Patrick A. Rodgers,"Pressure-volume-temperature relationships for
polymeric liquids: A review of equations of state and their characteristic
parameters for 56 polymers", Journal of Applied Polymer Science, 48, 1061-
1079(1993).
[17] Zhong , C. and H. Masuoka," Prediction of Henry's constants for
polymer-containing systems using the SRK equation of state coupled with a
new modified UNIFAC model ",Fluid Phase Equilibria,126,1-12(1996).
[18] Maloney, D. and J. Prausnitz,"Solubility of ethylene and other organic
solutes in liquid, low density polyethylene in the region 124 o to 300 o c",
AIChE Journal, 22,74-82(1976).
[19] Leonard , I. and D. Harnish, "Solubility of gases and liquids in molten
polystyrene", AIChE journal, 22, 117-121(1976).
[20] Liu, D. M. Prausnits,"Solubilities of volatile solutes in poly vinyl acetate
from 125 to 200oC", Journal of polymer science, 15, 145-153(1977).
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:53606", author = "Somayeh Tourani and Alireza Behvandi", title = "Prediction of Henry's Constant in Polymer Solutions using the Peng-Robinson Equation of State", abstract = "The peng-Robinson (PR), a cubic equation of state (EoS), is extended to polymers by using a single set of energy (A1, A2, A3) and co-volume (b) parameters per polymer fitted to experimental volume data. Excellent results for the volumetric behavior of the 11 polymer up to 2000 bar pressure are obtained. The EoS is applied to the correlation and prediction of Henry constants in polymer solutions comprising three polymer and many nonpolar and polar solvents, including supercritical gases. The correlation achieved with two adjustable parameter is satisfactory compared with the experimental data. As a result, the present work provides a simple and useful model for the prediction of Henry's constant for polymer containing systems including those containing polar, nonpolar and supercritical fluids.
", keywords = "Equation of state, Henry's constant, Peng-Robinson, polymer solution.", volume = "5", number = "4", pages = "297-5", }
