  Single three dimensional polymers confined to a slab, i.e. to the region
between two parallel plane walls, are studied by Monte Carlo simulations. They
are described by $N$-step walks on a simple cubic lattice confined to the
region $1 \le z \le D$. The simulations cover both regions $D << R_F$ and $D >>
R_F$ (where $R_F \sim N^\nu$ is the Flory radius, with $\nu \approx 0.587$), as
well as the cross-over region in between. Chain lengths are up to $N=80,000$,
slab widths up to D=120. In order to test the analysis program and to check for
finite size corrections, we actually studied three different models: (a)
Ordinary random walks (mimicking $\Theta$-polymers); (b) Self-avoiding walks
(SAW); and (c) Domb-Joyce walks with the self-repulsion tuned to the point
where finite size corrections for free (unrestricted) chains are minimal. For
the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with
Markovian anticipation. In addition to the partition sum (which gives us a
direct estimate of the forces exerted onto the walls), we measure the density
profiles of monomers and of end points transverse to the slab, and the radial
extent of the chain parallel to the walls. All scaling laws and some of the
universal amplitude ratios are compared to theoretical predictions.
