Chemistry Reference
In-Depth Information
Fig. 5 Illustration of the interpretation of the coarse grained models for polymers and solvent: In
the case of short alkanes, typically three C C bonds are taken together in one effective unit (
dotted
circle
). The oligomer C
16
H
34
, containing 50 atoms or 16 united atoms, is thus reduced to an
effective chain of five beads. Neighboring beads along a chain interact with a combination of LJ
and FENE potentials. Nonbonded beads only interact with a single LJ potential. The solvent
molecule (CO
2
in the present case) is represented by a point particle (in the case of CO
2
or C
6
H
6
,it
carries a quadrupole moment; in the case of NH
3
or H
2
S, it carries a dipole moment). From Yelash
et al. [
234
]
the softer potential
U
bond length
ð
r
Þ
a significantly larger MD time step can be applied
than when one uses (
2
), (
3
), etc.
Of course, when one deals with cooperative phenomena in a system containing
a great number of very long chains, even the use of the bond fluctuation model or
the bead spring model in simulations is a big effort. So the question arises: is even
a much coarser view of polymers useful? In the extreme case, a whole polymer
chain is represented by a (very soft) effective particle. Murat and Kremer [
188
]
suggested replacing the chains by soft ellipsoidal particles that can overlap strongly
in the melt to take into account the fact that in the volume
V
taken by one chain
of length
N
and radius
R
g
/
N
1
=
2
N
3
=
2
, there is space for a large number
;
V
/
ð/
N
1
=
2
Þ
of other chains because the monomer density of the considered chain
scales as
r /
N
1
=
2
.
The idea to coarse-grain the description of a system containing a very large
number of polymer chains such that each chain is represented by a single effective
particle dates back to the Asakura Oosawa model [
189 191
] of polymer colloid
mixtures. In this model, the colloidal particles (e.g., cross-linked polystyrene
spheres with radii in the size range 100 nm
N
=
V
/
1
m
m) are represented as hard
spheres, which have no other interactions than excluded volume interactions
between themselves and with the polymers. The polymers are taken as soft spheres
of radius
R
p
(which is thought to be of the order of the gyration radius of the chains)
and are treated like particles of an ideal gas (i.e., they may overlap with no energy
cost). The solvent molecules of these colloidal dispersions are not considered
explicitly. This model is extremely popular in colloid science (e.g., [
192 194
])
<
R
c
<
