We show that the average size of self-avoiding polygons (SAPs) with a fixed knot is much larger than that of no topological constraint if the excluded volume is small and the number of segments is large. We call it topological swelling. We argue an “enhancement” of the scaling exponent for random polygons with a fixed knot. We study them systematically through SAP consisting of hard cylindrical segments with various different values of the radius of segments. Here we mean by the average size the mean-square radius of gyration. Furthermore, we show numerically that the topological balance length of a composite knot is given by the sum of those of all constituent prime knots. Here we define the topological balance length of a knot by such a number of segments that topological entropic repulsions are balanced with the knot complexity in the average size. The additivity suggests the local knot picture.
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7 December 2017
Research Article|
December 01 2017
Scaling behavior of knotted random polygons and self-avoiding polygons: Topological swelling with enhanced exponent
Erica Uehara;
Erica Uehara
Department of Physics, Faculty of Core Research, Ochanomizu University
, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan
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Tetsuo Deguchi
Tetsuo Deguchi
Department of Physics, Faculty of Core Research, Ochanomizu University
, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan
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J. Chem. Phys. 147, 214901 (2017)
Article history
Received:
August 07 2017
Accepted:
October 13 2017
Citation
Erica Uehara, Tetsuo Deguchi; Scaling behavior of knotted random polygons and self-avoiding polygons: Topological swelling with enhanced exponent. J. Chem. Phys. 7 December 2017; 147 (21): 214901. https://doi.org/10.1063/1.4999266
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