## Abstract

A study was conducted to find that both total curvature and total torsion of the closed random polygon are not equal to π/2 per bond, but have corrections proportional to 1/n with universal coefficients close to 1.2 by using different methods. Many geometrical characteristics of closed polymer loops modeled as polygons of n > 1 edges. The joint probability distribution of all vectors was considered in the closed polygon to ensure the correct normalization. The study suggested that nπ/2n is an average angle of n turn for the polygon, because of the connection of smooth curves. It is concluded that both total curvature an total torsion deviates from the expected linear in n behavior and correction to both curvature and torsion do not depend on n because of opposite signs.

Original language | English (US) |
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Pages (from-to) | 4524-4527 |

Number of pages | 4 |

Journal | Macromolecules |

Volume | 41 |

Issue number | 12 |

DOIs | |

State | Published - Jun 24 2008 |

## ASJC Scopus subject areas

- Organic Chemistry
- Polymers and Plastics
- Inorganic Chemistry
- Materials Chemistry