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 κN-1. The conventional asymptotic formula, δQ(N→∞) approximately κN-1 Nγ-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.