Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Periodic copolymers at selective interfaces: A large deviations approach


Code(s) de Classification MSC:

Résumé: We analyze a (1+1)-dimension directed random walk model of a polymer dipped in a medium constituted by two immiscible solvents separated by a flat interface. The polymer chain is heterogeneous in the sense that a single monomer may energetically favor one or the other solvent. We focus on the case in which the polymer types are periodically distributed along the chain or, in other words, the polymer is constituted by identical stretches of fixed length. The phenomenon that one wants to analyze is the localization at the interface phenomenon: energetically favored configurations place most of the monomers in the preferred solvent and this can be done only if the polymer sticks close to the interface. We investigate, by means of Large Deviations, the energy-entropy competition that may lead, according to the value of the parameters (the strength of the coupling between monomers and solvents and an asymmetry parameter), to localization at the interface. We find a variational formula for the free energy of the system and we use it to analyze the phase diagram. We find in particular sharp bounds at small coupling parameter.

Mots Clés: Copolymers ; Localization--Delocalization Transition ; Energy-Entropy Competition ; Random Walk ; Large Deviations ; Donsker--Varadhan Theory

Date: 2003-10-01

Prépublication numéro: PMA-848