Chemistry Reference
In-Depth Information
ε
AA
r
AA
Fig. 3 Association potential as used in SAFT and PC SAFT
x
i
'
I
x
II
i
'
II
i
i
¼
(21)
which have to be fulfilled for all components
i
of the mixture.
3 Estimation of Model Parameters
Among the three pure-component parameters for nonassociating components there
are two parameters that are related to the size of the molecule: the segment diameter
s
and the segment number m. The third parameter, the energy parameter
e
, decribes
the attractive interactions between two molecules. For volatile components, these
parameters are determined by simultaneously fitting to physical properties, which
can on the one hand be calulated by an equation of state and are on the other hand
related to the size and the interactions of the molecules. Such properties are, e.g.,
liquid-density data (related to molecule size) and vapor pressures (related to the
intermolecular interactions). These parameters have already been determined for a
huge number of relevant solvents and can be found in extensive parameter tables, e.
g., in [
15
] (SAFT) and [
24
,
39
] (PC-SAFT).
However, polymers exhibit neither a measurable vapor pressure nor any other
property that can be directly related to the energy parameter. However, determining
all three parameters by fitting only to liquid-density data mostly does not yield
meaningful energy parameters that are suitable for binary calculations.
Considering the example of polycarbonate: in the literature only density data for
a polymer of unknown molecular weight are available [
40
]. Assuming the molecu-
lar weight (
M
w
) to be 100,000 g/mol, and fitting the three parameters for the SAFT
model to these data, one obtains
m
= 4043.5,
e
/
k
= 387.83 K and
v
00
= 17.114 cm
3
/mol
[
41
]. Since the segment number of polymers is proportional to their molecular
weight, the ratio
m
/
M
is usually fitted instead of the absolute segment number,
which led to
m
/
M
= 0.04043 for polycarbonate.
