Investigation of adsorption of polymer chains in disordered medium: Critical exponents and scaling
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
We investigate the influence of long-range correlated surface and
decaying near surface disorder on the process of adsorption of
long-flexible polymer chains with excluded volume interactions on
repulsive, inert and attractive walls. We consider a correlation
function for defects of the form $e^-z/\xir^a$ , where
$a<d-1$, $z$ being the coordinate in the direction perpendicular to
the surface, $r$ denotes the distance parallel to the surface. The
investigation is performed in the framework of renormalization group
field theoretical approach 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 in the
limit $m,n0$. In particular we study two limiting cases. First,
we investigate the scenario where the chain's extension it much
larger then $\xi$. Second, we consider the case where the chain's
extension is of the order of $\xi$. For both cases we obtained
series for bulk and the whole set of 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 volume
are studied. The obtained results indicate that long-range
correlated surface and decaying near the surface disorder
essentially influences the process of adsorption of long-flexible
polymer chains.