Entropic Sampling of Free and Ring Polymer Chains

Abstract

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.

A numerical technique for studying topological effects on the thermal properties of knotted polymer rings

“…The computational method has been checked using the trivial knot U as a test. We could repeat the previous results of [24] in the case of chains with lengths equal to 12, 30 and 50. …”

Entropic sampling of star-shaped polymers with different number of arms: temperature dependencies of structural properties

“…This method was successfully applied in our previous works [13,15,[19][20][21] as well as by other authors [4,12,[22][23][24] in polymer studies. An important attractive feature of this method is in its ability to obtain statistics for very rare events with relative ease.…”

“…Each i -th monomer has coordinates (x i , y i , z i ). The segments are being generated with the aid of semi-phantom random walks along the lattice with reverse steps being forbidden [15], contrary to the case of free (or phantom) walks. In order to change the configuration of the star, an arm and its k 0 -th monomer are randomly chosen and a new piece of this arm, starting from k 0 up to the end of the arm, is newly generated.…”

“…1. Specific excess entropy (relative to the phantom chain) as a function of the inverse number of segments for stars with different numbers of arms (3 ÷ 6), for a chain, and for ring [15].…”

“…For comparison, Fig. 1 presents the appropriate curve for ring chains [15] and it is seen that restrictions caused by closure of the chain are even greater than in the case of when the 6 arms were affixed to the center of the star.…”