Adsorption of polymer chains in a medium with different kinds of surface and bulk disorder

Frau Dr. Zoriana Usatenko

The process of adsorption of long-flexible polymer chains on an attractive, "marginal" and repulsive wall in the pure medium and in the medium with different kinds of surface and bulk disorder is investigated. Based on formal analogy of the polymer adsorption problem to the equivalent problem of critical phenomena in the semi-infinite |phi|^4 n-vector model of a magnet with a free surface we perform investigation in the framework of renormalization group field theoretical approach directly in d = 3 dimensions up to two-loop order for the semi-infinite |phi|^4 n-vector model in the limit n -> 0 (the case of pure medium without disorder) and up to first order of perturbation theory in a double (epsilon,delta)- expansion (epsilon = 4-d, delta = 3-a) for the semi-infinite |phi|^4 O(m; n) model with different types of surface and bulk disorder in the limit m; n -> 0. We perform the Pade and Pade-Borel resummation of the obtained series for the surface critical exponents, characterizing the process of adsorption of long-flexible polymer chains at the surface. The polymer linear dimensions parallel and perpendicular to the surface and the corresponding partition functions as well as the behavior of monomer density profiles and the fraction of adsorbed monomers at the surface and in the interior are studied. The obtained field-theoretical results at fixed dimensions d = 3 are in good agreement with recent Monte Carlo calculations for pure systems without disorder.

Frau Dr. Zoriana Usatenko,
Leibniz Institute of Polymer Research Dresden e.V.,
01069 Dresden, Germany
Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine,
UA 79011 Lviv, Ukraine
Marian Smoluchowski Institute of Physics, Jagellonian University, Department of Statistical Physics,
Reymonta 4, Krakow, Poland