Chemistry Reference
In-Depth Information
34 A for the CH CH bond. In this polymer, one also
needs two different bond-angle potentials (CH CH CH
2
and CH CH
2
CH
2
), and
four different torsional potentials (at the double bond differentiating
cis
from
trans
,
at the allyl bond next to the double bond in the
cis
and in the
trans
group, and at the
alkyl bond linking the monomers together).
Finally, we stress that the proper choice of atomistic model for the solvent
molecules could be a tricky problem. Consider, e.g., the case of (supercritical)
carbon dioxide (CO
2
), which plays an important role in chemical technology [
135
139
], e.g., as a blowing agent in the production of polymeric foams [
137 139
].
Despite longstanding efforts, there is no consensus in the literature on the
“best” effective potential describing the interaction between CO
2
molecules
[
131
]. Figure
2
presents data for liquid vapor coexistence [
130
] and the interfacial
tension [
130
]ofCO
2
, and compares them with various pertinent theoretical pre-
dictions (adapted from [
131
]). There have been many proposals on how to fully
parameterize all-atom potentials of this linear molecule [
140 152
], and coarse-
grained models have also been proposed [
53
,
131
,
153 155
]. Figure
2
presents a
counterpart to Fig.
1
, where experimental data for CO
2
are compared to various
theoretical predictions obtained from the computer simulation of such models
[
53
,
131
,
156
]. It is clearly seen that there still occur significant disagreements
between most of these computations and the experimental data (and there is also
disagreement between the theoretical models themselves). It is also clear that for
molecules such as CO
2
, which carry sizable quadrupole moment, a reduction to
ordinary point particles interacting with LJ forces and nothing else (as attempted in
[
53
]) is not a good choice, while amending this simple model with a (spherically
averaged) quadrupolar interaction [
131
] yields very satisfactory results. When
one takes the full quadrupolar interaction into account [
157
,
158
], no significant
improvement in the description of the equation of state is achieved, although
structural properties (such as orientational correlations among molecules) can be
accounted for more accurately [
158
]. Alternatively, one can get very accurate
description of equation of state data from computer simulation of a two-center
LJ model [
153 155
], but an atomistic interpretation of such a description is
also lacking.
For solvents such as ammonia (NH
3
) or hydrogen sulfide (H
2
S), it is important to
realize that such molecules carry a dipole moment
m
. If one uses an all-atom model,
it amounts to work with suitable partial charges on the sites of the atoms, and to deal
with Coulomb interactions between the atoms of different molecules. If one wants
to integrate hydrogen atoms in NH
3
or H
2
S into an united atom, as done for CH
2
or
CH
3
groups or methane, one can work with the Stockmayer model (SM) where the
molecules are treated as point particles interacting with LJ plus dipolar forces,
r
CH
2
CH bond, and
'
0
¼
1
:
m
i
being an unit vector in the direction of the dipole moment (which
has the strength
m
):
¼j~
r
i
~
r
j
j
,
12
6
2
s
ss
r
s
ss
r
m
3
r
2
m
i
V
SM
ð~
r
Þ¼
4
e
SS
þ
m
i
m
j
ð
~
r
Þ m
j
~
r
:
(6)
r
3
