Collapse of polymer brushes grafted onto planar ... - Wageningen UR

ADSORPTION OF PERIODIC AND RANDOM AB COPOLYMERS
L. Klushin 1,2) , E. Maraachlian 1) , A. Skvortsov 3)
1) American University of Beirut, Department of Physics, Beirut, Lebanon
2)
Institute for Macromolecular Compounds, Russian Academy of Sciences,
St. Petersburg, Russia
3)
Chemical-Pharmaceutical Academy, St. Petersburg, Russia
email: leo@aub.edu.lb
ABSTRACT
The goal of this work is to compare the effects of composition for random and periodic (multiblock) AB
copolymers on their localization at liquid-liquid and solid-liquid interfaces. Recently, it was extensively
demonstrated that random monomer distribution promotes localization of copolymers at liquid-liquid
interface as compared to periodic copolymers of the same average composition [1-3]. Here we
investigate the effects of composition on adsorption at a planar solid surface. The energy of contact for
a monomers A with the surface is ε , while the surface is assumed to be inert for monomers B
(ε = 0 ). The energy of interaction per monomer averaged over composition is thus ε = f ε , where f
B
is the fraction of A monomers. An ideal lattice chain model is used to calculate numerically the thermodynamic
average energy per segment and to determine the critical point of adsorption. We also
calculate the average thickness of the adsorbed layer.
For regular copolymers (periodic composition) in the range 1≤f ≤0.3,
the critical point of
adsorption is defined up to high accuracy by the composition average energy f ε = ε (homo) where
c c
ε (homo) is the critical energy for a homopolymer. This is in agreement with the earlier results of Di
c
Marzio et.al. [4]. We find that the dependence of the number of contacts and the thickness of the
adsorbed layer on ε in the vicinity of the critical point is well described by the analytical expressions
for a homopolymer with the effective energy per monomer ε .
For adsorption of random copolymers at a solid-liquid surface, a theory based on replica treatment
[5] predicts the critical adsorption energy to be lower than expected from simple composition average
arguments mentioned above, the deviation being especially prominent around f = 0.5. Our numerical
calculations for chains of polymerization index up to N = 10 4 show that the difference in the critical
energy between regular and random copolymers is quite negligible in the composition range
1≤f ≤0.5.
We develop an alternative analytical theory based on the trial potential approach
introduced in [3] that supports this result.
For lower values of f, (f < 0.2), the critical energy of adsorption for random copolymers becomes
noticeably lower than that for periodic chains. Both critical energies deviate significantly from the
simple composition average prediction. For periodic copolymers, the order parameter and the thickness
of the adsorbed layer as functions of ( ε − εс) εcare
still well described by “effective homopolymer”
expressions. For random copolymers, this description fails.
References
1. Sommer, J.-U., Daoud, M., 1995. Europhys. Let. 32, 407.
2. Dai, C.-A., et.al., 1994; 1995. Phys. Rev. Lett. 73, 2472; 74, 2837.
3. Chen, Z.Y., 1999; 2000. J. Chem. Phys. 111, 5603; 112, 8665.
4. Di Marzio, E.A., Guttman, C.M., Ma, A., 1995. Macromolecules 28, 2930.
5. Gutman, L., Chakraborty, A., 1995. J. Chem. Phys. 103, 10733.