Thermodynamics of anisotropic fluids using isotropic potentials Page: 4 of 5
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median potential results is very good in the range of den-
sities and temperatures studied. This is probably not
entirely unexpected as N2 is a good candidate for spher-
icalization , while 02 is only slightly more anisotropic,
as shown by its r*/l ratio .
To study the N2 + C02 mixture we used a simpli-
fied model for the CO2 molecule , that only takes
into account the oxygens as centers of force. While this
model may not be an accurate predictor of experimental
data, it does reproduce the basic anisotropy of the C02.
The length of the C02 molecule is lco2 = 2.32A, and
r*/lco2 _ 0.70, which makes it much more anisotropic
than either N2 or 02. The agreement between the rigid
rotor and the sphericalized potential results is limited to
smaller particle densities than in the case of N2 + 02.
(Note that a density of 2.3g/cm3 for N2 + CO2 yields
approximately the same particle density as 1.9g/cm3 in
the case of N2 + 02.)
median potential P(Ogcm') 2.9
* ~ 0 2.3
p 4 .9
d ~ 4 1.
FIG. 2. Test of median potentials for an equimolar
N2 + C02 mixture.
Perhaps the greatest advantage of the median poten-
tial over other effective spherical potentials  is the fact
that it is independent of density and temperature. The
success of the median recipe justifies in fact the analysis
and interpretation of experimental shock-wave data on
anisotropic fluids in terms of isotropic potentials. These
potentials, generally obtained by fitting Hugoniot data
[8-11], prove to be reliable in predicting thermodynamic
properties at high pressures and temperatures .
Given the success of the median, in particular for
molecules like N2 and 02, we therefore believe that such
potentials can be treated like medians and inverted to
yield atom-atom potentials. We carried out this task
for N2 and 02, by assuming an exp - 6 form for the
N - N and O - O interactions. This simple functional
form turns out to be sufficient for extracting with very
good accuracy atom-atom potentials from the N2 - N2
and 02 -02 intermolecular interactions. We show in Fig.
2 our O - O potential, together with an 0 - O potential
used to model solid state data of molecular 02 at high
pressures . The agreement is very good, showing that
unique sets of atom-atom potentials should perhaps be
sufficient to describe the thermodynamic properties of
simple anisotropic molecular systems in both fluid and
* based on Hugoniot data
based on solid-state data
.5 2 2.5 3
3 4 5 6 7 8
FIG. 3. O - O atom-atom potential based on shock and
solid phase data; repulsive region (top) and attractive region
The lower accuracy of the median for N2 + C02 mix-
tures, in particular at higher temperatures, can be largely
traced back to its performance in the case of pure C02
- see Fig. 3. Nevertheless, given the general success of
the median prescription, we would like to improve it in a
systematic way. Unfortunately, the basis for the median
construction is rather heuristic [2,5], and seems to defy a
full explanation [13,14].
To make progress, we turn to the observation that the
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Bastea, S & Ree, F H. Thermodynamics of anisotropic fluids using isotropic potentials, article, August 16, 1999; California. (digital.library.unt.edu/ark:/67531/metadc627772/m1/4/: accessed January 20, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.