Chemistry Reference
In-Depth Information
between analytic theory and computer experiments in this field [
10
-
14
] has proved
especially fruitful and instructive.
While the investigations mentioned above have been devoted exclusively to
homopolymers, the adsorption of copolymers (e.g., random or multiblock copoly-
mers) still poses open questions. Thus, for instance, the critical adsorption poten-
tial (CAP) dependence on block size
M
at fixed concentration of the sticking
A
-monomers is still unknown as are the scaling properties of
regular multiblock
copolymers
in the vicinity of the CAP. From the theoretical perspective, the case
of diblock copolymers has been studied by means of the grand canonical ensemble
(GCE) approach [
15
,
16
], within the self-consistent field (SCF) approach [
17
,
18
],
or by Monte Carlo computer simulations [
19
,
20
]. The case of
random copolymers
adsorption has gained comparatively more attention by researcher so far. It has been
investigated by Whittington et al. [
21
,
22
] using both the annealed and quenched
models of randomness. The influence of sequence correlations on the adsorption of
random copolymers has been treated by means of the variational and replica method
approach [
23
]. Sumithra and Baumgaertner [
24
] examined the question of how the
critical behavior of random copolymers differs from that of homopolymers. Thus,
among a number of important conclusions, the results of Monte Carlo simulations
demonstrated that the so-called adsorption (or, crossover) exponent
φ
(see below) is
independent of the fraction of attractive monomers
n
.
The adsorption kinetics of polymers has been intensively studied both experi-
mentally [
25
,
26
] and theoretically [
27
-
33
] since more than two decades now. A key
parameter thereby is the height of the free energy adsorption barrier that the polymer
chain has to overcome so as to bind to the surface. High barriers are usually referred
to as cases of
chemisorption
as opposed to those of
physisorption
which are char-
acterized by low barriers for adsorption. Depending on the strength of the binding
interaction
is of the
order of the thermal energy
k
B
T
(with
k
B
being the Boltzmann constant), and strong
physisorption when
, one distinguishes then between weak physisorption when
≥
2
k
B
T
. One of the important questions concerns the scaling
of the adsorption time
τ
ads
with the length of the polymer chain
N
in dilute solutions.
For homopolymers in the regime of strong physisorption (that is, for sticking energy
considerably above the CAP) computer experiments [
28
,
31
,
32
] suggest
N
α
τ
ads
∝
where
59. This result follows
from the assumed
zipping
mechanism in the absence of a significant barrier whereby
the chain adsorbs predominantly by means of sequential, consecutive attachment of
monomers, a process that quickly erases existing loops on the substrate. For the
case of
weak
adsorption, one should mention a recent study [
33
], where one finds
in contrast
α
is related to the Flory exponent
ν
as
α
=
1
+
ν
≈
1
.
37 which suggests shorter timescale for
surface attachment. In chemisorption, the high barrier which attaching monomers
encounter slows down the binding to the surface, the chain gains more time to attain
equilibrium conformation, and the adsorption process is believed to involve large
loop formation giving rise to
accelerated zipping
mechanism [
29
,
30
]. The predicted
value of
α
=
(
1
+
2
ν)/(
1
+
ν)
≈
1
.
02 [
32
]. A comprehensive
overview of experimental work and theoretic considerations may be found in the
recent review of O'Shaughnessy and Vavylonis [
30
].
α
in agreement with MC results is
α
≈
0
.
8
±
0
.
