## The Annals of Applied Probability

- Ann. Appl. Probab.
- Volume 15, Number 1B (2005), 963-983.

### Periodic copolymers at selective interfaces: A large deviations approach

Erwin Bolthausen and Giambattista Giacomin

#### Abstract

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 of identical stretches of fixed length. The phenomenon that one wants to analyze is the *localization at the interface*: 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. We express the free energy of the system in terms of a variational formula that we can solve. We then use the result to analyze the phase diagram.

#### Article information

**Source**

Ann. Appl. Probab., Volume 15, Number 1B (2005), 963-983.

**Dates**

First available in Project Euclid: 1 February 2005

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1107271674

**Digital Object Identifier**

doi:10.1214/105051604000000800

**Mathematical Reviews number (MathSciNet)**

MR2114996

**Zentralblatt MATH identifier**

1075.60123

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60F10: Large deviations 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]

**Keywords**

Copolymers localization–delocalization transition energy–entropy competition random walk large deviations Donsker–Varadhan theory

#### Citation

Bolthausen, Erwin; Giacomin, Giambattista. Periodic copolymers at selective interfaces: A large deviations approach. Ann. Appl. Probab. 15 (2005), no. 1B, 963--983. doi:10.1214/105051604000000800. https://projecteuclid.org/euclid.aoap/1107271674