Polymer pinning at an interface

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.

20 pages

Cited by in corpus (3)

• Smoothing effect of quenched disorder on polymer depinning transitions
• Random walk models and probabilistic techniques for inhomogeneous polymer chains
• Copolymer at selective interfaces and pinning potentials: weak coupling limits