Abstract
The free energy of a model of uniformly weighted lattice knots of length n and knot type K confined to a lattice cube of side length L-1 is given by F_{L}(ϕ)=-1/Vlogp_{n,L}(K), where V=L^{3} and where ϕ=n/V is the concentration of monomers of the lattice knot in the confining cube. The limiting free energy of the model is F_{∞}(ϕ)=lim_{L→∞}F_{L}(ϕ) and the limiting osmotic pressure of monomers leaving the lattice knot to become solvent molecules is defined by Π_{∞}(ϕ)=ϕ^{2}d/dϕ[F_{∞}(ϕ)/ϕ]. I show that, under very mild assumptions, the functions P_{L}(ϕ)=ϕ^{2}d/dϕ[F_{L}(ϕ)/ϕ]|_{n} and Π_{L}(ϕ)=ϕ^{2}d/dϕ[F_{L}(ϕ)/ϕ]|_{L} are finite-size approximations of Π_{∞}(ϕ).
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