Eur. Phys. J. B 2, 351-369 (1998)
https://doi.org/10.1007/s100510050259

On the number of intersections of self-repelling polymer chains

Fachbereich Physik der Universität Essen, 45117 Essen, Germany

Corresponding author: ^a smull@next17.theo-phys.uni-essen.de

Received: 1 April 1997
Revised: 24 October 1997
Accepted: 29 January 1998
Published online: 15 April 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.