Chemistry Reference
In-Depth Information
C
CC
C
C
C
C
C
C
C
C
C
C
C
C
C
Fig. 7 Definition of coarse grained repeat units (symbolized by
circles
) for the 1,4 polybutadiene
chain. The atomistic model is an united atom model of a random copolymer of 45%
cis
and 55%
trans
content, without vinyl units. Bond lengths are constrained
53 A for the CH
2
CH
2
bond,
ð'
1
:
5 A for the CH
2
CH bond and
34 A for the CH CH bond). From Strauch et al. [
117
]
'
1
:
'
1
:
coarse-grained (cg) effective monomers
i
,
j
. The intramolecular potentials
U
bond
ð
L
Þ
and
U
angle
ð
can be found by the “Boltzmann inversion” [
105 110
] from the
probability distribution
P
cos
YÞ
YÞ
of these degrees of freedom sampled from a
simulation of the full atomistic model. For this simulation of the full atomistic
model, a relatively short run of a relatively small system might suffice, at least in
favorable cases. Thus [
117
]:
ð
L
Þ
,
P
ð
cos
U
bond
ð
L
Þ¼
k
B
Tln
½
P
ð
L
Þ;
(12)
U
angle
ð
cos
YÞ¼
k
B
Tln
½
P
ð
cos
YÞ:
(13)
Figure
8
shows the resulting potentials at three temperatures. In principle,
effective potentials obtained from the Boltzmann inversion [(
12
) and (
13
)] will
contain entropic contributions and, hence, in general must be state-point dependent;
however, Fig.
8
suggests that in favorable cases this dependence is small.
However, it is difficult to obtain the nonbonded interaction from the same route:
in addition, atomistic potentials for nonbonded interactions are often rather unreli-
able. Thus, the form of the nonbonded interaction was chosen to be a priori fixed to
be of the LJ type:
U
c
LJ
ð
n
m
r
Þ¼
4
e
pp
ðs
pp
=
r
Þ
ðs
pp
=
r
Þ
(14)
