Handbook of Solvents - George Wypych - ChemTech - Ventech!

210 Christian Wohlfarth
B 1,B 2were refitted to the thermodynamic equilibrium data of pure methane, ethane, and
propane. 332 Both A nm matrices for PHC and COR equation of state contain different numerical
values. The remaining three characteristic parameters, c, T* and V 0, have to be adjusted
to experimental equilibrium data. Instead of fitting the c-parameter, one can also introduce a
parameter P* by the relation P* = cRT*/V 0. Characteristic parameters for many solvents
and gases are given by Chien et al. 332 or Masuoka and Chao. 334 Characteristic parameters of
more than 100 polymers and many solvents are given by Wohlfarth and coworkers, 335-348
who introduced segment-molar mixing rules and group-contribution interaction parameters
into the model and applied it extensively to polymer solutions at ordinary pressures as well
as at high temperatures und pressures, including gas solubility and supercritical solutions.
They found that it may be necessary sometimes to refit the pure-component characteristic
data of a polymer to some VLE-data of a binary polymer solution to calculate correct solvent
activities, because otherwise demixing was calculated. Refitting is even more necessary
when high-pressure fluid phase equilibria have to be calculated using this model.
A group-contribution COR equation of state was developed Pults et al. 349,350 and extended
into a polymer COR equation of state by Sy-Siong-Kiao et al. 351 This equation of
state is somewhat simplified by replacing the attractive perturbation term by the corresponding
part of the Redlich-Kwong equation of state.
PV
RT
( y −1)
( )
3
( y −1)
2
2
4y −2y
⎛α
−1⎞3y
+ 3αy − α + 1 aT ( )
= 1+ + c⎜
⎟
−
[4.4.96]
3
⎝ 2 ⎠
RTV
[ + bT ( )]
where:
a attractive van der Waals-like parameter
b excluded volume van der Waals-like parameter
c degree of freedom parameter, related to one chain-molecule (not to one segment)
y packing fraction
α accounts for the deviations of the dumbbell geometry from a sphere
Exponential temperature functions for the excluded volume parameter b and the attractive
parameter a were introduced by Novenario et al. 352-354 to apply this equation of state
also to polar and associating fluids. Introducing a group-contribution concept leads to segment-molar
values of all parameters a, b, c which can easily be fitted to specific volumes of
polymers. 351,354
The statistical associating fluid theory (SAFT) is the first and the most popular approach
that uses real hard-chain reference fluids, including chain-bonding contributions. Its
basic ideas have been developed by Chapman et al. 256-258 Without going into details, the final
SAFT equation of state is constructed from four terms: a segment term that accounts for
the non-ideality of the reference term of non-bonded chain segments/monomers as in the
equations shown above, a chain term that accounts for covalent bonding, and an association
term that accounts for hydrogen bonding. There may be an additional term that accounts for
other polarity effects. A dispersion term is also added that accounts for the perturbing potential,
as in the equations above. A comprehensive summary is given in Praunsitz’s book. 49
Today, there are different working equations based on the SAFT approach. Their main differences
stem from the way the segment and chain terms are estimated. The most common
version is the one developed by Huang and Radosz, 355 applying the fourth-order perturbation
approach as in COR or PHC above, but with new refitted parameters to argon, as given