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Theory

This page does not contain a full review of the theoretical background of the Perturbed-Chain SAFT equation of state. For further in-depth information please consult the author.

modelmol.jpgLarge progress in modeling phase behavior of polymer systems was made during the last years with use of equations of state. In many such theories chain-like molecules are modeled as chains of freely-jointed spherical segments. This molecular model is schematically illustrated on the right. According to this model, molecules are determined by three pure component parameters:

  • segment diameter s (the equivalent parameter to s is in the original SAFT model the segment volume v00)
  • segment number m
  • and attraction parameter e (the parameter e is in the original SAFT equation of state termed u0)

Despite its simplicity, this molecular model accounts for the essential characteristics of real molecules. Those characteristics are:

  •     repulsive interactions
  •     non-spherical shape of molecules (chain formation)
  •     attractive interactions (dispersion)

Despite considerable work on further developments, one of the most successful models remains the original SAFT equation of state. However, in the dispersion term of the original SAFT model, the chain-like structure of polymer compounds is not taken into account.


In the Perturbed-Chain SAFT equation of state, the dispersive forces are accounted for applying a perturbation theory of second order (Barker and Henderson), using an expression for the radial pair distribution function of a hard-chain reference fluid.


The equation of state is tested against computer simulation data of square-well chains. Excellent results are obtained for mixtures of short chains.


For application of the PC-SAFT equation of state to real substances, the integral in the dispersion term is replaced by a power series in density, where the coefficients show a simple dependence on segment number. These coefficients are refitted to pure component properties of alkanes from methane to triacontane.


The PC-SAFT equation of state requires three pure component parameters and is applied to mixtures with one-fluid mixing rules. Comparison to the original SAFT equation of state reveals significant improvement for both, mixtures of small components and polymer solutions.


You may view a short survey of the equations for calculation of the compressibility factor and the Helmholtz free energy.



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Foto von Prof. Dr. Gabriele Sadowski

Prof. Dr. Gabriele Sadowski

Adresse:

TU Dortmund
Fakultät Bio- und Chemieingenieurwesen
Emil-Figge-Str. 70
44227 Dortmund

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