Chemistry Reference
In-Depth Information
monomers are rotated together to new positions, thus restricting the torsional angle
to
60
and 180
) and nonlocal ones (slithering-snake moves or “pivot rotations”
[
165
]) have been implemented [
185
]. However, for the application of MD techni-
ques (one of the principle advantages of off-lattice models in comparison with
lattice models of polymers is [
81 84
] that MD accounts better for dynamic proper-
ties) models without such constraints for bond lengths and angles are more conve-
nient. To avoid the small MD time step that the (rather stiff) potentials for bond
lengths and bond angles [(
1
) and (
2
)] necessitate, one uses coarse-grained bead
spring models with rather soft “springs”. The most commonly used “spring poten-
tial” is the finitely extensible nonlinear elastic (FENE) potential [
75
,
78
,
186
,
187
]:
k
2
R
0
ln
1
r
2
R
0
U
FENE
ð
r
Þ¼
=
;
(10)
where the parameters
k
;
R
0
can be chosen as
k
¼
7,
R
0
¼
2[
186
]oras
k
¼
30
;
R
0
¼
5[
84
], for instance when one chooses a (truncated and shifted) LJ potential
[such as (
4
) and (
5
)] and measures lengths in units of
s
and energies in units of
e
pp
(we use here indices “pp” to distinguish these interactions from those of the
solvent). Note that in this model the LJ potential [(
4
) and (
5
)] acts between
any pair of monomers, including nearest neighbors along a chain; thus the total
potential for the length of an effective bond is in fact the sum of (
5
) and (
10
),
U
bond length
ð
1
:
, whereas between nonbonded pairs only (
5
)
acts. Although the minimum of (
5
) occurs at
U
ij
ð
r
Þ¼
U
ij
þ
U
FENE
ð
r
Þ
2
1
=
6
r
¼
r
min
Þ
with
r
min
¼
s
pp
,
r
0
min
Þ
the minimum of the bond potential occurs at [
84
]
U
bond length
ð
r
¼
with
r
0
min
r
0
min
does not fit to
any simple crystal structure is responsible for the occurrence of glass-like freezing-
in of this bead spring model at low temperatures. At densities
rs
r
0
min
and that the ratio
r
min
=
0
:
96
s
pp
. The fact that
r
min
6¼
3
pp
¼
1, the glass
transition occurs roughly at
k
B
T
g
=e
pp
-temperature (i.e.,
the temperature at which in the dilute limit very long bead spring chains collapse
into a dense globule) is much higher, namely
k
B
Y=e
pp
0
:
4[
84
], whereas the
Y
3[
10
]. Thus, for many
applications of the bead spring model based on (
4
), (
5
) and (
10
), the glass-like
behavior at low temperatures does not restrict its use in computer simulations. It
has the advantage that both MC and MD methods are readily applicable for its
study [
10
,
84
].
This bead spring model is an appropriate description for a very flexible chain,
but an analog of the bond angle potential [(
2
) in the atomistic model or (
9
) for the
bond fluctuation model], is not included here for simplicity. However, when one
adjusts
e
pp
; s
pp
to the vapor liquid critical temperatures and densities of short
alkanes, as done for methane (Fig.
1
), one obtains a rather good description of
vapor liquid coexistence data and the interfacial tension over a broad temperature
range [
56
] (Fig.
4
). Although it is known that alkanes do have a bond angle potential
for the C C bonds, it is ignored here because the simple bead spring model based
on (
10
) makes sense only if the effective monomers correspond to larger units
formed by integrating several (e.g., about
n
3
:
¼
3) carbon atoms in one unit. Thus,
the bond potential
U
bond length
ð
r
Þ
defined above does not represent a single (stiff!)
