Influence of long-range correlated surface and near the surface disorder on the process of adsorption of long-flexible polymer chains

TL;DR

This paper investigates how long-range correlated surface and near-surface disorder affect the adsorption behavior of long-flexible polymer chains using a renormalization group field theoretical approach, providing new insights into surface critical phenomena.

Contribution

It introduces a theoretical framework analyzing the impact of correlated disorder on polymer adsorption, deriving surface critical exponents for different chain extension scenarios.

Findings

Derived series for surface critical exponents.

Analyzed polymer dimensions and monomer density profiles.

Compared effects for chain extension larger or comparable to correlation length .

Abstract

The influence of long-range correlated surface and decaying near surface disorder with quenched defects is studied. We consider a correlation function for the defects of the form $\frac{e^{-z/\xi}}{r^{a}}$, where $a<d-1$ and $z$ being the coordinate in the direction perpendicular to the surface and $r$ denotes the distance parallel to the surface. We investigate the process of adsorption of long-flexible polymer chains with excluded volume interactions on a "marginal" and attractive wall in the framework of renormalization group field theoretical approach 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 the above mentioned type of surface and near the surface disorder in the limit $m,n\to 0$. 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.