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Functional self-similarity, scaling and a renormalization group calculation of the partition function for a non-ideal chain

Author

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  • Altenberger, Andrzej R.
  • Siepmann, J.Ilja
  • Dahler, John S.

Abstract

The hypothesis of asymptotic self-similarity for nonideal polymer chains is used to derive the functional and differential equations of a new renormalization group. These equations are used to calculate the partition functions of randomly jointed chains with hard-sphere excluded-volume interactions. Theoretical predictions are compared with Monte Carlo calculations based on the same microscopic chain model. The excess partition function converges very slowly to its true asymptotic form δQ(N→∞)∼κN−1. The conventional asymptotic formula, δQ(N→∞)∼κN−1Nγ−1, is found to be applicable for chains of moderate length and for excluded-volume interactions appropriate to the subclass of flexible self-avoiding chains.

Suggested Citation

  • Altenberger, Andrzej R. & Siepmann, J.Ilja & Dahler, John S., 2001. "Functional self-similarity, scaling and a renormalization group calculation of the partition function for a non-ideal chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(1), pages 107-136.
    • Handle: RePEc:eee:phsmap:v:289:y:2001:i:1:p:107-136
    DOI: 10.1016/S0378-4371(00)00325-3
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