Excluded Volume Effect in Polymer Chains

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Abstract
A new Monte Carlo method for the statistical study of the polymer chain excluded volume problem is presented. Random chains which are not allowed to have closed loops of fewer than R links are generated. Results of calculations for diamond lattice chains of up to 5000 links with R up to 1000 are given and discussed. These chain lengths are rather longer than those which have been studied previously. This is possible because (a) volume exclusion applies not to the entire chain, but only to the ``sliding segment'' of R links, and (b) a chain is not rejected when it comes back on itself, but forced not to cross and weighted appropriately. Results closely approximating the correct ones for the completely restricted random walk chain are obtained for R∼100. Results on number of configurations for long chain lengths and ring formation and trapping probabilities are given.

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