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

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

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4 Scopus citations

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 languageEnglish (US)
Pages (from-to)107-136
Number of pages30
JournalPhysica A: Statistical Mechanics and its Applications
Volume289
Issue number1-2
DOIs
StatePublished - 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.

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