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Summary:We extend Monte Carlo (MC) methods developed in our previous paper (J. Phys. A, Math. Gen. 2004, 37, 1573 and based on entropic sampling within Wang-Landau (WL) algorithm to the simulation of lattice and continuous models of ring polymers. For a continuous freely joined ring chain (an equilateral polygon) with hard sphere monomer units, the excess entropy of rings relative to the corresponding reference system, a phantom ring chain, is obtained. The excess specific entropy is calculated for a set of various diameters of monomer units d and chain lengths N. Its limiting values for N → ∞ (N −1 → 0) are estimated for each d and coincidence with those for corresponding free chains is demonstrated. We also develop a WL approach to calculate thermal properties of free and ring continuous chains with an LennardJones attraction between nonbonded beads being added to hard core repulsion at fixed d. The obtained energy distributions provide calculation of canonical properties such as conformational energy, heat capacity, entropy, and mean square radius of inertia. Thermal results for free and ring chains are being finally compared. Analogous calculations are performed for lattice-free chains and rings.

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By means of a variant of the Monte Carlo method (entropic sampling within the Wang-Landau algorithm) the models of the interaction of a neutral polymer with a flat surface are studied. The method yields distribution functions over the energy and the distance from the polymer to the surface. Based on these distributions, excess entropies of the systems and their thermal properties are calculated: internal energy, heat capacity, average radius of gyration, average chain end-to-end distance, and average distance from the polymer to the surface. Continuous and lattice models are considered.

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