### 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 |

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### ASJC Scopus subject areas

- Materials Chemistry

### Cite this

*Macromolecules*,

*41*(12), 4524-4527. https://doi.org/10.1021/ma800299c

**Total curvature and total torsion of a freely jointed circular polymer with n ≫ 1 segments.** / Grosberg, Alexander Y.

Research output: Contribution to journal › Article

*Macromolecules*, vol. 41, no. 12, pp. 4524-4527. https://doi.org/10.1021/ma800299c

}

TY - JOUR

T1 - Total curvature and total torsion of a freely jointed circular polymer with n ≫ 1 segments

AU - Grosberg, Alexander Y.

PY - 2008/6/24

Y1 - 2008/6/24

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=47249163351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=47249163351&partnerID=8YFLogxK

U2 - 10.1021/ma800299c

DO - 10.1021/ma800299c

M3 - Article

VL - 41

SP - 4524

EP - 4527

JO - Macromolecules

JF - Macromolecules

SN - 0024-9297

IS - 12

ER -