Summary: We apply a new simulation technique proposed in Wang and Landau (WL) Phys. Rev. Lett. 86, 2050 (2001)] to sampling of three-dimensional lattice and continuous models of polymer chains. Distributions obtained by homogeneous (unconditional) random walks are compared with results of entropic sampling (ES) within the WL algorithm. While homogeneous sampling gives reliable results typically in the range of 4-5 orders of magnitude, the WL entropic sampling yields them in the range of 20-30 orders and even larger with comparable computer effort. A combination of homogeneous and WL sampling provides reliable data for events with probabilities down to 10-35.
For the lattice model we consider both the athermal case (self-avoiding walks, SAWs) and the thermal case when an energy is attributed to each contact between nonbonded monomers in a self-avoiding walk. For short chains the simulation results are checked by comparison with the exact data. In WL calculations for chain lengths up to \(N=300\) scaling relations for SAWs are well reproduced. In the thermal case distribution over the number of contacts is obtained in the \(N\)-range up to \(N=100\) and the canonical averages – internal energy, heat capacity, excess canonical entropy, mean square end-to-end distance – are calculated as a result in a wide temperature range.
The continuous model is studied in the athermal case. By sorting conformations of a continuous phantom freely joined \(N\)-bonded chain with a unit bond length over a stochastic variable, the minimum distance between nonbonded beads, we determine the probability distribution for the \(N\)-bonded chain with hard sphere monomer units over its diameter a in the complete diameter range, \(0 \leq a \leq 2\), within a single ES run. This distribution provides us with excess specific entropy for a set of diameters a in this range. Calculations were made for chain lengths up to \(N = 100\) and results were extrapolated to \(N \to \infty\) for a in the range \(0 \leq a \leq 1.25\).