Chemistry Reference
In-Depth Information
10
-4
(a)
t = 0
t = 0.33
t = 1.63
t = 3.28
t = 6.55
t = 8.19
t = 9.83
N=256
ε
/k
B
T =4
.0
5*10
-5
0
0
50
100
150
200
250
300
l(t)
Fig. 8.9
(
a
) Distribution of tail size for different times (in units of 10
5
MCS) during the polymer
chain adsorption for a chain with
N
=
256 at
/
k
B
T
=
4
.
0. (
b
) The same as in (
a
) as derived
from the solution of the ME for chain length
N
=
32. For better visibility the time slices for
t
1, 5, 30 100, 150, 200, and 300 are shifted along the time axis and arranged such that the initial
distribution for
t
=
=
1 is represented by the most distant slice
in Fig.
8.8
b indicates, the PDF of loops is also described by an exponential function.
The PDFs for loops at different time collapse on a master curve, if scaled appro-
priately with the instantaneous order parameter
n
(
)/
t
N
. Eventually, in Fig.
8.9
a
(
,
)
we present the observed PDF
T
of tails for different times
t
after the start of
adsorption and compare the simulation results with those from the numeric solution
of (
8.17
), taking into account that
T
l
t
. One may readily verify
from Fig.
8.9
that the similarity between simulational and theoretic results is really
strong. In both cases one starts at
t
(
l
,
t
)
=
P
(
N
−
l
,
t
)
=
1 with a sharply peaked PDF at the full tail
length
l
N
. As time proceeds, the distribution becomes broader and its
maximum shifts to smaller values. At late times the moving peak shrinks again and
the tail either vanishes or reduces to a size of single segment which is expressed by
the sharp peak at the origin of the abscissa.
(
t
=
1
)
=
8.5 Summary
The main focus of this contribution has been aimed at the adsorption transition of
random and regular multiblock copolymers on a flat structureless substrate whereby
by different means - scaling considerations and computer simulations - a consistent
picture of the macromolecule behavior at criticality is derived.
As a central result one should point out the phase diagram of regular multi-
block adsorption which gives the increase of the critical adsorption potential
c
with decreasing length
M
of the adsorbing blocks. For very large block length,
M
−
1
→
0, one finds that the CAP approaches systematically that of a homogeneous
polymer.
The phase diagram for random copolymers with quenched disorder which gives
the change in the critical adsorption potential,
p
c
, with changing percentage of the
sticking
A
-monomers,
p
, is observed to be in perfect agreement with the theoreti-
