Handbook of Solvents - George Wypych - ChemTech - Ventech!

214 Christian Wohlfarth
4.4.4.3 Comparison and conclusions
The simple Flory-Huggins χ-function, combined with the solubility parameter approach
may be used for a first rough guess about solvent activities of polymer solutions, if no experimental
data are available. Nothing more should be expected. This also holds true for any
calculations with the UNIFAC-fv or other group-contribution models. For a quantitative
representation of solvent activities of polymer solutions, more sophisticated models have to
be applied. The choice of a dedicated model, however, may depend, even today, on the nature
of the polymer-solvent system and its physical properties (polar or non-polar,
association or donor-acceptor interactions, subcritical or supercritical solvents, etc.), on the
ranges of temperature, pressure and concentration one is interested in, on the question
whether a special solution, special mixture, special application is to be handled or a more
universal application is to be found or a software tool is to be developed, on numerical simplicity
or, on the other hand, on numerical stability and physically meaningful roots of the
non-linear equation systems to be solved. Finally, it may depend on the experience of the
user (and sometimes it still seems to be a matter of taste).
There are deficiencies in all of these theories given above. These theories fail to account
for long-range correlations between polymer segments which are important in dilute
solutions. They are valid for simple linear chains and do not account for effects like chain
branching, rings, dentritic polymers. But, most seriously, all of these theories are of the
mean-field type that fail to account for the contributions of fluctuations in density and composition.
Therefore, when these theories are used in the critical region, poor results are often
obtained. Usually, critical pressures are overestimated within VLE-calculations. Two other
conceptually different mean-field approximations are invoked during the development of
these theories. To derive the combinatorial entropic part correlations between segments of
one chain that are not nearest neighbors are neglected (again, mean-field approximations
are therefore not good for a dilute polymer solution) and, second, chain connectivity and
correlation between segments are improperly ignored when calculating the potential energy,
the attractive term.
Equation-of-state approaches are preferred concepts for a quantitative representation
of polymer solution properties. They are able to correlate experimental VLE data over wide
ranges of pressure and temperature and allow for physically meaningful extrapolation of experimental
data into unmeasured regions of interest for application. Based on the experience
of the author about the application of the COR equation-of-state model to many
polymer-solvent systems, it is possible, for example, to measure some vapor pressures at
temperatures between 50 and 100 o C and concentrations between 50 and 80 wt% polymer by
isopiestic sorption together with some infinite dilution data (limiting activity coefficients,
Henry’s constants) at temperatures between 100 and 200 o C by IGC and then to calculate the
complete vapor-liquid equilibrium region between room temperature and about 350 o C,
pressures between 0.1 mbar and 10 bar, and solvent concentration between the common
polymer solution of about 75-95 wt% solvent and the ppm-region where the final solvent
and/or monomer devolatilization process takes place. Equivalent results can be obtained
with any other comparable equation of state model like PHC, SAFT, PHSC, etc.
The quality of all model calculations with respect to solvent activities depends essentially
on the careful determination and selection of the parameters of the pure solvents, and
also of the pure polymers. Pure solvent parameter must allow for the quantitative calculation
of pure solvent vapor pressures and molar volumes, especially when equation-of-state