Modeling of Polymer Phase Equilibria Using Equations of State

  • Gabriele SadowskiEmail author
Part of the Advances in Polymer Science book series (POLYMER, volume 238)


The most promising approach for the calculation of polymer phase equilibria today is the use of equations of state that are based on perturbation theories. These theories consider an appropriate reference system to describe the repulsive interactions of the molecules, whereas van der Waals attractions or the formation of hydrogen bonds are considered as perturbations of that reference system. Moreover, the chain-like structure of polymer molecules is explicitly taken into account. This work presents the basic ideas of these kinds of models. It will be shown that they (in particular SAFT and PC-SAFT) are able to describe and even to predict the phase behavior of polymer systems as functions of pressure, temperature, polymer concentration, polymer molecular weight, and polydispersity as well as – in case of copolymers – copolymer composition.


Copolymers Equation of state Modeling Polymers Solubility Sorption Thermodynamics 



Helmholtz energy


Parameter of the van der Waals equation


Fraction of bonds between segments α and β within a copolymer


Parameter of the van der Waals equation


Temperature-dependent segment diameter


Radial distribution function


Value of the radial distribution function at contact


Boltzmann constant


Molecular weight


Molecular weight of pseudocomponent j


Number average of molecular weight


Weight average of molecular weight


z-Average of molecular weight

\( \overline {{M^k}} \)

kth moment of the molecular weight distribution


Segment number

\( \bar{m} \)

Average segment number


Number of molecules


Number of association sites per molecule or monomer unit


Mole number


Binary interaction parameter




Ideal gas constant






Molar volume


Segment volume (parameter of SAFT)


Mole fraction of component i (solvent or polymer)


Mole fraction of pseudocomponent j within polymer


Continuous molecular weight distribution


Weight fraction of component i


Weight fraction of pseudocomponent j in polymer


Compressibility factor


Fraction of segments α or β in a copolymer



High-density polyethylene






Low-density polyethylene




Molecular weight distribution




Perturbed Chain Statistical-Associating-Fluid Theory




Perturbed Hard-Chain Theory


Perturbed Hard-Sphere-Chain Theory


Perturbed Soft-Chain Theory


Statistical-Associating-Fluid Theory


SAFT with Variable Range



Greek Letters


Segment type


Dispersion energy parameter


Association-energy parameter


Reduced density


Association volume parameter


Number density (molecules per volume)


Temperature-independent segment diameter


Fugacity coefficient of component i in the mixture


Fugacity coefficient of polymer pseudocomponent j in the mixture



Contribution due to association


Contribution due to chain formation


Dispersion (van der Waals attraction)


Dispersion contribution according to the PC-SAFT model


Hard-chain contribution


Hard-sphere contribution


Ideal gas








Phases I and II


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Biochemical and Chemical Engineering, Laboratory for ThermodynamicsTU DortmundDortmundGermany

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