Chemistry Reference
In-Depth Information
and:
m
1
m
1
m
2
a
i
¼
a
0
i
þ
a
1
i
þ
a
2
i
ð
analogously for
b
i
Þ
(17)
m
m
m
; e
ij
¼ e
i
e
j
1
2
s
i
þ s
j
p
s
ij
¼
1
k
ij
(18)
a
0
i
,
a
1
i
,
a
2
i
,
b
0
i
,
b
1
i
and
b
2
i
in (
17
) are model constants and are given in Table
1
.
k
ij
in (
18
) is again a binary parameter that corrects for deviation from the geometric
mean mixing rule and has to be determined by fitting to binary experimental data.
The Helmholtz energy change due to the formation of hydrogen bonds (associa-
tion) is captured by
A
assoc
. A detailed description as well as the corresponding
expressions can be found, e.g., in [
12
]. The main assumption is that association can
be described by a short-range but very strong association potential (Fig.
3
). This
leads to two more parameters required for the modeling of an associating molecule:
the association volume
k
AA
(corresponds to the potential width
r
AA
) and the associ-
ation strength
e
AA
(the potential depth).
For application, one needs to define the number
N
* of so-called association sites,
meaning the number of donor and acceptor sites respectively, by which a molecule is
able to form hydrogen bonds. Different association sites may have different associ-
ation parameters (in most cases they are assumed to be identical). Details can be
again found in [
12
] and [
14
].
Moreover, Helmholtz energy expressions are available that can account for
interactions due to dipole moments [
30 32
], quadrupole moments [
33 35
], or
even charges [
36 38
] of the molecules. They have already been successfully applied
in combination with SAFT or PC-SAFT but will not be considered within this work.
Given the expression for the Helmholtz energy, other thermodynamic properties
needed for phase-equilibrium calculations can be derived by applying textbook
thermodynamics. Thus, system pressure and the chemical potentials of the mixture
components can be obtained by applying the following relations:
¼
@
A
p
(19)
@
V
T;n
i
and
A
res
@
@
pV
NkT
RT
ln
'
i
¼
i
RT
ln
z
with
z
¼
(20)
n
i
T;V;n
j6
Phase-equilibrium calculations are finally performed using the classical phase-
equilibrium conditions:
