Mean field and the confined single homopolymer

We develop a statistical model for a confined homopolymeric chain molecule based on a monomer grand ensemble representation. The molecule is subject to a confining external field, a backbone interaction, and an attractive interaction between any pair of monomers. An exact minimum principle for the thermodynamics of the backbone in an external field is obtained, and a controlled mean field approximation results in a modified minimum principle from which relevant physical quantities such as monomer density can be found. We explore the limit in which the chain is subject to tight confinement, and make a preliminary investigation of a prototypical system.