Size distribution of ring polymers
Abstract
We present an exact solution for the distribution of sample averaged monomer to monomer distance of ring polymers. For noninteracting and localinteraction models these distributions correspond to the distribution of the area under the reflected Bessel bridge and the Bessel excursion respectively, and are shown to be identical in dimension d ≥ 2, albeit with pronounced finite size effects at the critical dimension, d = 2. A symmetry of the problem reveals that dimension d and 4  d are equivalent, thus the celebrated Airy distribution describing the areal distribution of the d = 1 Brownian excursion describes also a polymer in three dimensions. For a selfavoiding polymer in dimension d we find numerically that the fluctuations of the scaled averaged distance are nearly identical in dimension d = 2, 3 and are well described to a first approximation by the noninteracting excursion model in dimension 5.
 Publication:

Scientific Reports
 Pub Date:
 June 2016
 DOI:
 10.1038/srep27661
 arXiv:
 arXiv:1501.06151
 Bibcode:
 2016NatSR...627661M
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Statistical Mechanics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 Supplementary Material added at the end of text