The exact solution of a three-dimensional lattice polymer confined in a slab with sticky walls

We present the exact solution of a three-dimensional lattice model of a polymer confined between two sticky walls, that is within a slab. We demonstrate that the model behaves in a similar way to its two-dimensional analogues and agrees with Monte Carlo evidence based upon simulations of self-avoiding walks in slabs. The model on which we focus is a variant of the partially directed walk model on the cubic lattice. We consider both the phase diagram of relatively long polymers in a macroscopic slab and the effective force of the polymer on the walls of the slab. PACS numbers: 05.50.+q, 64.60.De (Some figures in this article are in colour only in the electronic version)