Chain length and density dependence of the chemical potential of lattice polymers

The chemical potential of lattice polymers is calculated in two alternative ways: by the Widom insertion method using the Rosenbluth and Rosenbluth sampling technique and by the modified Widom method, based on the insertion of one segment to an existing polymer chain. In the first part of this paper we present a detailed derivation of the modified Widom technique for lattice systems. We then proceed to calculate the chemical potential for chains of up to 50-mers in monomeric and polymeric solvents. We observe marked odd-even effects on the chemical potential. The density dependence of the chemical potential is found to vary with chain length. For most temperatures and densities studied the chemical potential of chain molecules in a fixed environment becomes linear in chain length for molecules longer than 10-20 segments. The results are compared to the classical lattice theories, which are found to be best at high densities, as expected based on previous investigations.