Chemistry Reference
In-Depth Information
Fig. 15 Isothermal slices
through the phase diagram of
the CO
2
þ
C
5
H
12
system at
T
423
:
48 K (a) and
T
344
:
34 K (b).
Closed
circles
represent
experimental data [
270
],
asterisks
MC results for the
coarse grained model, and the
solid curve
the corresponding
TPT1 MSA prediction. The
dashed curve
shows, for
comparison, the TPT1 MSA
prediction for a CO
2
model
with no quadrupole moment
(
q
c
0). The
triangle
indicates MC results for the
critical point. From Mognetti
et al. [
56
]
slices in the plane of variables pressure versus molar concentration of CO
2
are
shown, and one can see that the two-phase coexistence regions show up as loops
extending from pure pentane to rather large CO
2
content, but not reaching pure CO
2
since at these temperatures CO
2
is supercritical. Remarkably, the MC results agree
better with experiment than the TPT1-MSA calculation at all molar concentrations.
Although one expects that TPT1-MSA overestimates the critical pressure
p
c
some-
what, for
T
48 K this overestimation occurs by a factor of about two! It is
also interesting to note that TPT1-MSA is also inaccurate for the high pressure
branch of the two-phase coexistence loop, although for small CO
2
content the data
are far away from any critical region. Since TPT1-MSA here is based on exactly the
same interaction parameters as the MC simulation, this discrepancy indicates some
shortcoming of TPT1-MSA beyond its inability to accurately describe the critical
region.
It also is obvious that ignoring the quadrupolar interaction among CO
2
mole-
cules yields less accurate results, as expected from the experience with pure CO
2
.
Figure
16
now considers the behavior of the mixtures of CO
2
and hexadecane,
which was already used as a generic system for testing simulation methodologies
[
10
,
53
]. However, in that work the quadrupolar interactions were ignored, and an ad
hoc correction factor
x
¼
423
:
886 for the Lorentz Berthelot combining rule was used
in order to get qualitatively reasonable results that agreed almost quantitatively with
experiment. Including the quadrupolar interactions
0
:
ð
q
c
¼
0
:
47
Þ
but leaving
x ¼
1
has about the same effect as choosing
x ¼
9 in the model without quadrupolar
effects. A rather small deviation of
x
from unity would clearly bring the data for
q
c
¼
0
:
47 further upward, and hence create agreement with the experimental data.
Of course, one cannot expect that the simple Lorentz Berthelot combining rule (
30
)
0
:
