  A compressed knotted ring polymer in a confining cavity is modelled by a
knotted lattice polygon confined in a cube in ${\mathbb Z}^3$. The GAS
algorithm [17] is used to sample lattice polygons of fixed knot type in a
confining cube and to estimate the free energy of confined lattice knots.
Lattice polygons of knot types the unknot, the trefoil knot, and the figure
eight knot, are sampled and the free energies are estimated as functions of the
concentration of monomers in the confining cube. The data show that the free
energy is a function of knot type at low concentrations, and (mean-field)
Flory-Huggins theory [12,15] is used to model the free energy as a function of
monomer concentration. The Flory interaction parameter of knotted lattice
polygons in ${\mathbb Z}^3$ is also estimated.
