polymer pinning at an interface

Nicolas Pétrélis (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

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.

Mots clés: Polymers; Localization-Delocalization Transition; Pinning; Random Walk; Wetting

Domaines: Probabilités [math.PR]

Nicolas Pétrélis. polymer pinning at an interface. 2005. ⟨hal-00004784⟩