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The European Physical Journal B
ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)
Abstract Volume 2 Issue 3 (1998) pp 351-369
On the number of intersections of self-repelling polymer chains
S. Müller (a), L. Schäfer
Fachbereich Physik der Universität Essen, 45117 Essen, Germany
Received: 1 April 1997 / Revised: 24 October 1997 / Accepted: 29 January 1998
Abstract: We give a detailed analysis of the intersection properties of polymers. Using the renormalization group we provide a full crossover function for the dependence of the number of intersections in a single polymer on chain length and excluded volume strength. We compare our results with Monte-Carlo data and with exact calculations for a random walk, finding good agreement in all respects. Restricting to the vicinity of the eight ternary fixed points we also calculate the number of intersections between two chains placed at a fixed distance, including the two halves of a block-copolymer. The analysis of these systems confirms the interpretation of the different contributions to the number of intersections in a single chain. Due to the highly nontrivial character of the correlations in a polymer chain the correction exponents in both cases however are different. None of the results can be extracted from any Flory-type estimate.
PACS. 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 36.20.Ey Conformation (statistics and dynamics)
(a) email: smull@next17.theo-phys.uni-essen.de
Online publication: May 27, 1998
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