Chemistry Reference
In-Depth Information
Chapter 8
Polymer Chain Adsorption on a Solid Surface:
Scaling Arguments and Computer Simulations
A. Milchev, V. Rostiashvili, S. Bhattacharya, and T. Vilgis
Abstract
We examine the phase transition of polymer adsorption as well as the
underlying kinetics of polymer binding from dilute solutions on a structureless solid
surface. The emphasis is put on the properties of regular multiblock copolymers,
characterized by block size
M
and total length
N
as well as on random copolymers
with quenched composition
p
of sticky and neutral segments. The macromolecules
are modeled as coarse-grained bead-spring chains subject to a short-ranged surface
adhesive potential. Phase diagrams, showing the variation of the critical threshold
for single chain adsorption in terms of
M
and
p
, are derived from scaling consid-
erations in agreement with results from computer experiment. Using both scaling
analysis and numerical data from solving a system of coupled master equations, we
demonstrate that the phase behavior at criticality and the adsorption kinetics may
be adequately predicted and understood, in agreement with the results of extensive
Monte Carlo simulations. Derived analytic expressions for the mean fraction of
adsorbed segments as well as for probability distribution functions of the various
structural building blocks (i.e., trains, loops, tails) at time
t
during the chain attach-
ment process are in good agreement with our numeric experiments and provide
insight into the mechanism of polymer adsorption.
8.1 Introduction
The adsorption of polymers on solid surfaces is a long-standing problem which
plays an important role in a number of applications in technology (protective coat-
ings, adhesives, lubricants, stabilization of colloids, flocculation, etc.) and biology
(adsorption of biopolymers, etc.). As a phenomenon it poses a number of challeng-
ing scientific problems [
1
-
4
] too. Important theoretical contributions have been
made by Birshtein [
5
], de Gennes [
6
], and Eisenriegler et al. [
7
]. Later studies
have covered adsorption of polyelectrolytes [
8
], dynamics of adsorbed chains [
9
],
and adsorption on chemically heterogeneous surfaces [
10
]. The close relationship
