  We study a model of a semiflexible long chain polymer confined to a
two-dimensional slit of width $w$, and interacting with the walls of the slit.
The interactions with the walls are controlled by Boltzmann weights $a$ and
$b$, and the flexibility of the polymer is controlled by another Boltzmann
weight $c$. This is a simple model of the steric stabilisation of colloidal
dispersions by polymers in solution. We solve the model exactly and compute
various quantities in $(a,b,c)$-space, including the free energy and the force
exerted by the polymer on the walls of the slit. In some cases these quantities
can be computed exactly for all $w$, while for others only asymptotic
expressions can be found. Of particular interest is the zero-force surface --
the manifold in $(a,b,c)$-space where the free energy is independent of $w$,
and the loss of entropy due to confinement in the slit is exactly balanced by
the energy gained from interactions with the walls.
