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We extend the Monte Carlo methods developed in our previous papers [J. Phys. A 37, 1573 (2004); Macromol. Theory-Simul. 14, 491 (2005)] and based on entropic sampling within the Wang-Landau algorithm to simulation of a lattice model of flexible polyelectrolytes. We consider a strongly charged polyelectrolyte chain accompanied by neutralizing counterions on a simple cubic lattice with periodic boundary conditions. The Coulomb potential and the excluded volume condition between different ions or beads are taken into account. The obtained energy distributions make possible the calculation of canonical properties such as conformational energy, heat capacity, entropy, free energy, and mean-square end-to-end distance over a wide temperature range in a single simulation.

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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Inspired by recent advances on the self-assembly of non-spherical nanoparticles, Monte Carlo simulations of the packing and thermodynamic properties of truncated nanocubes and cuboctahedra have been performed. The ergodicity problem was overcome by a modified Wang-Landau entropic sampling algorithm and equilibrium structural and thermodynamic properties were computed over a wide density range for both non-interacting and interacting particles. We found a structural transition from a simple cubic to a rhombohedral order when the degree of truncation exceeds a value of 0.9.