Chemistry Reference
In-Depth Information
In the present contribution we focus on copolymer physisorption, extending thus
the aforementioned studies of homopolymers statics and kinetics. We show how
scaling analysis as well as different MC simulation methods help understand the
critical behavior of multiblock and random copolymers. It turns out that the crit-
ical behavior of these two types of copolymers can be reduced to the behavior
of an effective homopolymer chain with “renormalized” segments. For multiblock
copolymers one can thus explain how the adsorption threshold depends on the block
length
M
and even derive an adsorption phase diagram in terms of CAP against
M
.
In the case of random copolymers, the sequence of sticky and neutral (as regards the
solid substrate) monomers within a particular chain is usually fixed which exempli-
fies a system with
quenched randomness
. Nevertheless, close to criticality the chain
is still rather mobile, so that the sequence dependence is effectively averaged over
the time of the experiment and the problem can be reduced to the easier case of
annealed randomness
. We show that the MC findings close to criticality could be
perfectly described within the annealed randomness model.
For both regular multiblock and random copolymers, we compare the predicted
kinetics of adsorption in the regime of strong physisorption, to consistent numeric
data derived from simulations and coupled master equations. We demonstrate that
the observed adsorption kinetics is close to that of homopolymers and suggest inter-
pretation of typical deviations. Eventually, we should like to stress that the complex
polymer hydrodynamics near an interface has remained beyond the scope of this
chapter.
8.2 Simulation Methods
Apart from the frequently used bond fluctuation method (BFM) [
28
,
32
], two
coarse-grained models, a bead-spring off-lattice model [
9
] and a cubic lattice model
implementing the so-called pruned-enriched Rosenbluth method (PERM) [
14
], are
used to test theoretical predictions.
8.2.1 Off-Lattice Bead-Spring Model
In our computer simulations we use a coarse-grained off-lattice bead-spring
model [
11
] to describe polymer chains. The system consists of a single chain teth-
ered at one end to a flat structureless surface so as to avoid problems with transla-
tional entropy depending on the box size. There are two kinds of monomers: “A” and
“B,” of which only the “A” type feels an attraction to the surface. The surface inter-
action of the “A”-type monomers is described by a short-range square well potential
U
w
(
)
=
<δ
and
U
w
(
)
=
δ
=
.
125
(in units of the maximal bond length extension
l
max
between adjacent beads). The
effective bonded interaction is described by the FENE (finitely extensible nonlinear
elastic) potential:
z
for
z
z
0 otherwise, whereby the range
0
