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A
hs
A
chain
A
disp
,
SAFT
A
assoc
+
+
+
Fig. 1 Helmholtz energy contributions of SAFT
analytical expressions are available for
A
ref
A
hs
and
p
ref
p
hs
¼
¼
for hard-sphere
systems (e.g., Carnahan and Starling [
11
]).
Deviations of real molecules from the reference system may occur, e.g., due to
attractive interactions (dispersion), formation of hydrogen bonds (association), or
the nonspherical shape of the molecules (which can be understood as the formation
of chains from spherical segments). These contributions are usually assumed to be
independent of each other and are accounted for by different perturbation terms.
Depending on the kind of considered perturbation and on the expression used for its
description, different models have been developed. One of the first models derived
from that idea was the Statistical-Associating-Fluid Theory (SAFT) (Chapman
et al. [
12
,
13
]; Huang and Radosz [
14
,
15
]).
In SAFT, a chain-like molecule (solvent molecule or polymer) is assumed to be a
chain of m identical spherical segments. Starting from a reference system of m hard
spheres (
A
hs
), this model considers three perturbation contributions: chain forma-
tion (
A
chain
), attractive interactions of the (nonbonded) segments (
A
disp
), and asso-
ciation via a certain number of association sites (
A
assoc
) (Fig.
1
):
A
res
mA
hs
A
chain
|
{z
}
A
hc
mA
disp
;
SAFT
A
assoc
¼
þ
þ
þ
(5)
The Carnahan Starling formulation is used for
A
hs
; the segment segment
dispersion
A
disp
is described using a fourth-order power series with respect to
reversed temperature (Chen and Kreglewski [
16
]); and the contribution of chain
formation and the association term are based on the work of Wertheim [
17
].
Subsequently, various perturbation theories were developed that are also based
on (
5
) but differ in the specific expressions used for the different types of perturba-
tions. Examples are the Perturbed Hard-Sphere-Chain Theory (PHSC) ([
18
,
19
]),
SAFT-VR [
20
], and models proposed by Chang and Sandler [
21
], Hino and
Prausnitz [
22
], and Blas and Vega [
23
].
A widely used model of this kind is the Perturbed Chain SAFT (PC-SAFT)
model [
24 26
], which was particularly developed to improve the modeling of
chain-like molecules, e.g., polymers. As the main improvement, PC-SAFT con-
siders the hard chain as a reference system, which is of course much more
appropriate for polymers and other chain-like molecules than the hard-sphere
