Lattice models for confined polymers

Abstract

Self-avoiding chains on regular lattices are frequently used as models to study thermodynamic properties of linear polymers, particularly regarding critical phenomena which may occur in these systems. We review these models, concentrating on their properties under geometric constraints, when the walks are placed inside strips or pores. In these cases the models may be solved using a transfer matrix formalism for the generating functions. A short range interaction between the sites visited by the walks and the walls is included in the model and the distribution of the sites and the forces on the walls are studied as functions of the strength of this interaction.