Polymer pinning at an interface

TL;DR

This paper investigates the localization transition of a hydrophobic homopolymer at an oil-water interface using a random walk model, developing a new method to bound the critical curve from below.

Contribution

It introduces a novel strategy that considers the polymer targeting high-reward sites to better bound the critical curve for localization transition.

Findings

Derived a lower bound for the critical curve separating localized and delocalized phases.

Showed the importance of targeting high-reward sites in the polymer's localization behavior.

Provided insights into the competition between energetic gains and random rewards in polymer localization.

Abstract

In this article, I study the localization transition of an hydrophobic homopolymer in interaction with an interface between oil and water. To that aim I consider a model in which the trajectories of a simple random walk play the role of the possible configurations of the polymer. The chain gains an energetic factor for every monomer it puts in the oil and receives a random price of positive average each time it touches the origin. So a competition arises between this two effects to know wether the chain is delocalized in the oil or if it stays localized in the neighborhood of the interface. As usual a critical curve divides the phase spaces in a localized and a delocalized area, and the point of my paper is to develop a new strategy to bound this critical curve by below. To achieve this result I take into account the fact that the polymer can target the sites where it comes back to the origin to receive prices as high as possible.