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.
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Received: 1 April 1997 / Revised: 24 October 1997 / Accepted: 29 January 1998
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Müller, S., Schäfer, L. On the number of intersections of self-repelling polymer chains. Eur. Phys. J. B 2, 351–369 (1998). https://doi.org/10.1007/s100510050259
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DOI: https://doi.org/10.1007/s100510050259