  We study the localisation of lattice polymer models near a permeable
interface in two dimensions. Localisation can arise due to an interaction
between the polymer and the interface, and can be altered by a preference for
the bulk solvent on one side or by the application of a force to manipulate the
polymer. Different combinations of these three effects give slightly different
statistical mechanical behaviours. The canonical lattice model of polymers is
the self-avoiding walk which we mainly study with Monte Carlo simulation to
calculate the phase diagram and critical phenomena. For comparison, a solvable
directed walk version is also defined and the phase diagrams are compared for
each case. We find broad agreement between the two models, and most minor
differences can be understood as due to the different entropic contributions.
In the limit where the bulk solvent on one side is overwhelmingly preferred we
see how the localisation transition transforms to the adsorption transition;
the permeable interface becomes effectively an impermeable surface.
