Handbook of Solvents - George Wypych - ChemTech - Ventech!

206 Christian Wohlfarth
wi mass fraction of component i
There has been a broad application of this group-contribution UNIFAC-fv concept to
polymer solutions in the literature. Raetzsch and Glindemann 290 recommended the use of
the real free-volume relation from the Flory-Orwoll-Vrij model to account for realistic
PVT-data. Problems arise for mixtures composed from chemically different components
that posses the same groups, e.g., mixtures with different isomers. Kikic et al. 291 discussed
the influence of the combinatorial part on results obtained with UNIFAC-fv calculations.
Gottlieb and Herskowitz 292,293 gave some polemic about the special use of the c1-parameter within UNIFAC-fv calculations. Iwai et al. 294,295 demonstrated the possible use of
UNIFAC-fv for the calculation of gas solubilities and Henry’s constants using a somewhat
different free-volume expression. Patwardhan and Belfiore 296 found quantitative discrepancies
for some polymer solutions. In a number of cases UNIFAC-fv predicted the occurrence
of a demixing region during the calculation of solvent activities where experimentally only
a homogeneous solution exists. Price and Ashworth 297 found that the predicted variation of
residual solvent activity with polymer molecular mass at high polymer concentrations is opposite
to that measured for polydimethylsiloxane solutions. But, qualitative correct predictions
were obtained for poly(ethylene glycol) solutions with varying polymer molecular
mass. 298-300 However, UNIFAC-fv is not capable of representing thermodynamic data of
strongly associating or solvating systems.
Many attempts have been made to improve the UNIFAC-fv model which cannot be
listed here. A comprehensive review was given by Fried et al. 301 An innovative method to
combine the free-volume contribution within a corrected Flory-Huggins combinatorial entropy
and the UNIFAC concept was found by Elbro et al. 302 and improved by Kontogeorgis
et al. 303 These authors take into account the free-volume dissimilarity by assuming different
van der Waals hard-core volumes (again from Bondi’s tables 264 ) for the solvent and the
polymer segments
13 / 13 / ( , )
fv
V = q V −V
i
fv
ϕ i
i i i vdW
= i
fv
i ∑
j
fv
j j
3
[4.4.92a]
xV / xV
[4.4.92b]
where:
qi surface area of component i based on Bondi’s van der Waals surfaces
xi mole fraction of component i
Vi molar volume of component i
Vi,vdW van der Waals hard-core molar volume of component i
and introduced these free-volume terms into Equation [4.4.68] to obtain a free-volume corrected
Flory-Huggins combinatorial term:
or
fv
fv ( i xi) ( i xi)
fv
lnγ = ln ϕ / + 1 − ϕ /
[4.4.93a]
i
fv
fv
( ϕiwi) ( ϕi
xi)
fv
lnΩ i = ln / + 1 − /
[4.4.93b]