Computer simulation of the free energy of polymer chains with excluded volume and with finite interactions

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Abstract
We have recently suggested an approximate computer simulation technique, based on the scanning method, which enables one to extract the entropy (and hence the free energy) of polymer chains from a relatively small sample. So far this technique has been discussed in terms of chains with excluded volume (EV); in the present work we extend its scope to chains, which also have finite interactions. In order to obtain better approximations for the entropy we utilize the concepts of the generalized Monte Carlo procedure suggested by Schmidt [Phys. Rev. Lett. 51, 2175 (1983)] (and discussed in the preceding paper). We analyze our results from the preceding paper for self-attracting random walks (without EV) on square and simple-cubic lattices, and show that our techniques lead to accuracy which is better than 0.3% for both the free energy and the entropy. For chain models which include EV, we use, in addition to Schmidt’s procedure, an alternative one based on ‘‘importance sampling.’’ We test these two procedures as applied to self-avoiding walks (SAW’s) on a square lattice, where the SAW’s are unbounded in space or bounded in relatively small ‘‘boxes.’’ Very accurate results for the entropy are also obtained here. It turns out, however, that importance sampling is slightly more efficient than the Schmidt procedure.