## 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→∞) approximately κ^{N-1}. The conventional asymptotic formula, δQ(N→∞) approximately κ^{N-1} N^{γ-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.

Original language | English (US) |
---|---|

Pages (from-to) | 107-136 |

Number of pages | 30 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 289 |

Issue number | 1-2 |

DOIs | |

State | Published - 2001 |

### Bibliographical note

Funding Information:This research has been supported by grants from the Theoretical and Computational Chemistry Program of the National Science Foundation. JIS gratefully acknowledges financial support through a Dreyfus New Faculty Award and a McKnight/Land-Grant Assistant Professorship. We also acknowledge grants of computer time from the Minnesota Supercomputer Institute. Finally, we are indebted to Professor Pierre-Gilles de Gennes for helpful correspondence.

Copyright:

Copyright 2017 Elsevier B.V., All rights reserved.