Chemistry Reference
In-Depth Information
may attribute to the rather small values of the block length
M
that were accessible
in our simulation. One should also allow for scatter in the end time of the shoulder
due to the mismatch in the capture times of all the successive
A
-blocks in the course
of our statistical averaging over many chains during the computer experiment.
Somewhat surprisingly,
α
which describes the scaling of the total adsorption time
N
α
, is observed to
decline
as the block size
M
is increased -
in contrast to the general trend of regular multiblock copolymers which resemble
more and more homopolymers (where
with polymer size,
τ
∝
.
Evidently, the frequent disruption of the zipping process for smaller blocks
M
slows
down the overall adsorption.
In the case of random copolymers, Fig.
8.7
b, the transients resemble largely
those of a homopolymer chain with the same number of beads again, apart from the
expected difference in the plateau height which is determined by the equilibrium
number of adsorbed monomers. A rescaling of the vertical axis with the fraction
of sticking monomers,
p
, however, does not lead to coinciding plateau heights -
evidently the loops, whose size also depends on
p
, affect the equilibrium number of
adsorbed monomers. The variation of the observed scaling exponent
α
=
1
+
ν
), as the block size
M
→∞
α
with compo-
α
≈
.
α
sition
p
is shown in the inset to Fig.
8.7
b wherefrom one gets
being
largely independent of
p
. Note that this value is considerably lower than the power
of 2
1
6 with
24 which has been observed earlier [
28
], however, for very short chains with
only 10 sticking beads. One may conclude that even for random copolymer adsorp-
tion the typical time of the process scales as
.
N
α
, as observed for homopolymers
and regular block copolymers. It is conceivable, therefore, that an
effective
zipping
mechanism in terms of renormalized segments, that is, segments consisting of an
A
and
B
diblock unit of length 2
M
for regular multiblock copolymers, provides
an adequate notion of the way the adsorption kinetics may be treated even in such
τ
∝
10
3
2.0
(b)
10
5
N=256
ε
(a)
10
3
Slope
=
1.49
1.8
/k
B
T=4.0
ε
/k
B
T=4.0
1.6
10
4
1.4
1.2
10
3
10
2
10
100
0.2
0.4
0.6
0.8
1
10
2
M
p
Homo
M=1
M=2
M=4
M=8
M=16
M=32
M=64
1.5
10
1
1.4
p=0.25
p=0.50
p=0.75
p=1.00
10
1
1.3
1.2
1.1
0
10
20
M
10
0
10
0
10
3
10
4
10
5
10
6
10
7
10
3
10
4
10
5
10
6
10
7
t [MCS]
t [MCS]
Fig. 8.7
(
a
) Number of adsorbed segments,
N
ads
(
t
))
, vs time
t
for regular
AB
-copolymers with
block size
M
256. For comparison, the transient of a homopolymer
is shown by a
solid line
too. The time interval, taken by the initial “shoulder,” is shown in the
upper left inset
.The
lower inset
displays the variation of the scaling exponent,
=
1-64 and length
N
=
α
, for the time of
N
α
vs block length relationship. (
b
) The same as in (
a
) but for random copolymers
adsorption
τ
∝
of length
N
=
256 and different composition
p
=
0
.
25
,
0
.
5
,
0
.
75. For
p
=
1 one has the case of
a homopolymer. The
inset
shows the variation of
α
with
p
