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In-Depth Information
Fig. 14
Top
: Profiles of the orientational order parameter
S
ð
z
Þ
(
s shaped curves
), and of the
volume fraction of lattice sites taken by monomeric units,
fð
z
Þ
(
thick lines
), for a bond fluctuation
model (see Sect.
2.2
) on the 80
80
1000 simple cubic lattice, and chain length
N
20, with
N
01.
Squares
indicate
the density values at coexistence and
open circles
indicate the order parameter at the transition.
These values were extracted from a bulk grand canonical simulation [
123
]. The
inset
shows an
enlarged plot of the transition region.
Bottom
: Two dimensional
xz
map of the coarse grained
order parameter profile for a system snapshot corresponding to the graph. From Ivanov et al. [
123
]
1
;
600 chains in the system, choosing parameters
f
8
:
0(
9
) and
l
g
0
:
carrying a quadrupole moment (Fig.
2
). It has also been shown that the angular
dependence of the quadrupole quadrupole interaction can be averaged, with no
significant loss in accuracy, as far as the phase behavior is concerned. Similarly, the
phase diagrams of the pure alkanes are well accounted for by a bead spring model
(Figs.
4
and
5
), ignoring bond angle and torsional potentials.
In this section, we ask the question: to what extent can one obtain a reasonable
description of the phase behavior of mixtures, when one has a accurate description
of the pure material? For a binary mixture (A,B), some information on the interac-
tions between chemically distinct species is indispensable, and we use the simplest
assumption for this purpose, namely the Lorentz Berthelot combining rule (
30
).
This means that we wish to
predict
the phase behavior of the mixture, given some
knowledge of the pure components. The question to what extent this works is highly
nontrivial: of course, if one allows for sufficiently many additional parameters, an
accurate “fitting” of experimental vapor liquid coexistence data clearly is achiev-
able, but such an approach is rather ad hoc and has little predictive power, and
hence is unsatisfactory.
As an example, Fig.
15
compares simulations [
56
] of this model for the mixture
of carbon dioxide and pentane to pertinent experimental data [
270
]. Two isothermal
