Monte Carlo Study of Coiling-Type Molecules. I. Macromolecular Configurations

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Abstract
Monte Carlo methods have been employed on a high-speed digital computer to generate samples of random chains intended to simulate polymer molecules. The chains were generated on a tetrahedral lattice subject to the excluded-volume effect using both normal methods and procedures biased in favor of the more tightly coiled chains. Nonbonded nearest-neighbor interactions were counted and, by introducing an appropriate potential energy of interaction between such neighbors, a partition function was established. For N link chains, the mean-square end-to-end distances, 〈RN2〉, and the mean-square radii of gyration, 〈SN2〉, were calculated as functions of temperature. Using the ratio 〈RN2〉/N as a criterion, it is found that a Flory Θ temperature exists; it is also found that the observed ratio 〈SN2〉/〈RN2〉 is compatible with the Θ temperature concept. Finally, there are reported distribution functions for the end-to-end separations and for material densities of polymers subject to the excluded-volume effect but without other intramolecular interactions.

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