Chemistry Reference
In-Depth Information
A
hc
A
disp, PC-SAFT
A
assoc
+
+
Fig. 2 Helmholtz energy contributions of PC SAFT
system (Fig.
2
). The hard-chain system is obtained as in SAFT as the sum of the
hard-sphere and chain-formation contributions
A
hs
and
A
chain
. Since the dispersion
term
A
disp,PC-SAFT
now describes the attraction of chain molecules rather than that
of nonbonded segments, it appears to be a function of chain length
m
:
A
res
A
hc
A
disp
;
PC SAFT
A
assoc
¼
þ
ð
m
Þþ
(6)
Modeling with PC-SAFT (as well as with original SAFT and related models)
requires three pure-component parameters for a nonassociating molecule. As for the
above-mentioned van der Waals equation, these parameters have a physical mean-
ing. The first parameter of PC-SAFT is the segment diameter
s
(SAFT uses the
segment volume
v
00
), which corresponds to the van der Waals parameter
b
.
Parameter
e
is the energy related to the interaction of two segments, corresponding
to the van der Waals parameter
a
. The third parameter considers the deviation from
the spherical shape of the molecules: the segment number
m
. In the case of a
polymer molecule, the latter is proportional to the molecular weight. To describe a
binary system, again an additional binary parameter (
k
ij
) is used to correct for
deviations of the geometric mean of the energy parameter.
According to (
6
), different expressions are used to describe the various con-
tributions within the PC-SAFT model. The hard-chain contribution reads as:
X
ln
g
ii
d
ii
A
hc
NkT
¼
m
A
hs
NkT
x
i
m
i
ð
1
Þ
(7)
i
"
#
3
2
3
2
A
hs
NkT
¼
1
z
0
3
z
1
z
2
1
z
z
Þ
þ
2
þ
3
z
0
ln 1
ð
z
3
Þ
(8)
ð
z
3
2
z
z
3
1
ð
z
3
Þ
X
m
¼
x
i
m
i
(9)
i
6
r
X
i
x
i
m
i
d
i
;
z
n
¼
z
3
¼
(10)
