Chemistry Reference
In-Depth Information
Fig. 7 Liquid liquid equilibrium of polypropylene/
n
pentane at three temperatures (polypropyl
ene:
M
w
= 50.4 kg/mol,
M
w
/
M
n
= 2.2). Comparison of experimental cloud points (
symbols
)[
47
]
with PC SAFT calculations (
lines
)[
25
].
k
ij
= 0.0137. The polymer was assumed to be monodis
perse with
M
w
being the molecular weight
in the modeling. As polymers of different molecular weight consist of the same type
of monomers (segments) and differ in the number of monomers (corresponds to
segment number) only, the only parameter that needs to be changed for polymers of
different molecular weights is the segment number. The latter is already given as
function of molecular weight (see Table
2
), which makes it easy to account for
different molecular weights. Figure
8
presents solubility curves for polyethylene
(LDPE) in ethene as a function of the polymer molecular weight. The same set of
parameters for polyethylene (Table
2
) was used to describe the whole range of
molecular weights using PC-SAFT. As can be seen, the model captures the influ-
ence of the molecular weight very well and is thus able to predict the phase behavior
as function of the polymer length.
Similarly to Fig.
5b
for vapor liquid equilibria, Fig.
9
illustrates the ability of
PC-SAFT to model liquid liquid equilibria of LDPE dissolved in a variety of
solvents. The amount of polymer is about 5 wt% for all cases. Using PC-SAFT,
the experimental cloud points can be described with high accuracy. Although for
each system only one binary temperature-independent parameter is used, the model
even captures the changing slope of the cloud-point curves, from a negative slope
for ethene and ethane to the positive slope for C
3
and C
4
solvents.
The modeling can, of course, also be extended to systems containing more than
two components. In this case, it is assumed that the phase behavior in ternary or
higher systems is still dominated by binary interactions. This means that only
binary interactions are accounted for and the modeling is completely based on the
pure-component and binary parameters determined before for the pure substances
and binary subsystems, respectively.
