On the number of intersections of self-repelling polymer chains |
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Authors: | S Müller L Schäfer |
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Institution: | Fachbereich Physik der Universit?t Essen, 45117, Essen, Germany
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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.
Received: 1 April 1997 / Revised: 24 October 1997 /
Accepted: 29 January 1998 |
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Keywords: | PACS 64 60 Ak Renormalization-group fractal and percolation studies of phase transitions - 36 20 Ey Conformation (statistics and dynamics) |
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