Eur. Phys. J. E 1, 9-25
Adsorption of a Gaussian random copolymer chain at an interface
X. Châtellier - J.-F. Joanny
Institut Charles Sadron, 6 rue Boussingault, 67083 Strasbourg, France
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Received 21 January 1999
Abstract
We consider the adsorption of an isolated, Gaussian, random, and quenched
copolymer chain at an interface. We first propose a simple analytical method
to obtain the adsorption/depletion transition, by averaging over the disorder
the partition function instead of the free energy. The adsorption thresholds
obtained by previous authors at a solid/liquid and at a liquid/liquid interface
for multicopolymer chains can be rederived using this method. We also compare
the adsorption thresholds obtained for bimodal and for Gaussian disorder;
they only agree for small disorder. We focus on the specific case of an ideally
flat asymmetric liquid/liquid interface, and consider the situation where the
chain is composed of monomers of two different chemical species A and B.
The replica method is developed for this case. We show that the Hartree approximation,
coupled to a replica symmetry assumption, leads to the same adsorption thresholds
as obtained from our general method. In order to describe the properties of
the adsorbed (or depleted) chain, we develop a new approximation for long chains,
within the framework of the replica theory. In most cases, the behavior of
a random copolymer chain can be mapped onto that of a homopolymer chain at
an asymmetric attractive interface. The values of the effective adsorption
energy are different for a random and a periodic copolymer chain. Finally,
we consider the case of uncorrelated annealed disorder. The behavior of an
annealed chain can be mapped onto that of a homopolymer chain at an asymmetric
non attractive interface; hence, an annealed chain cannot adsorb at an asymmetric
interface.
PACS
05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems -
68.10.-m Fluid surfaces and fluid-fluid interfaces -
82.65.Dp Thermodynamics of surfaces and interfaces
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag
