Critical adsorption of polymers in a medium with long-range correlated quenched disorder

Abstract

We investigated the influence of short- and long-range correlated quenched disorder introduced into the medium on the process of adsorption of long-flexible polymer chains on a wall by using the field theoretical approach in $d=4-ε$ and the directly in d=3 dimensions up to one-loop order for the semi-infinite $|ϕ^4|$ m-vector model (in the limit $m \to 0$) with a boundary. This allows us to describe the critical behaviour of long-flexible polymer chains in the vicinity of the surface and to obtain the whole set of surface critical exponents at the special surface transition ($c=c_{ads}$), which separates the nonadsorbed region $c>c_{ads}$ from the adsorbed one $c<c_{ads}$. In the case of very strong correlation of the disorder we obtained that a polymer collapses and adsorbs on a wall. The obtained results indicate that for the systems with long-range correlated quenched disorder the new set of surface critical exponents arises and show that polymer chains in solution with that type of disorder adsorb on a wall stronger than the polymer chains in pure medium.

7 pages