### Abstract

A polymer of finite length is embedded on a diamond lattice where the angle between adjacent monomers is cos^{-1}(-1/3)=109°. We show that the characteristic function C_{n} (k) can be calculated in closed form for an n link chain if all configurations (i.e., trans and gauche) are given equal weights. It is necessary to do a spherical average to get rid of the cubic symmetry artifically imposed by the diamond lattice. This represents the only model, other than the freely jointed chain, for which the characteristic function is known in closed form. This model may be regarded as the lattice version of the freely rotating chain. From the characteristic function we extract the first few moments 〈R^{2}〉_{n}, 〈R^{4}〉_{n}, and 〈R^{6}〉 _{n}. We show that the results for the second and fourth moments are identical to those for the freely rotating chain, but the sixth moment is different. Various approximations to the probability distribution function W_{n} (R) [the Fourier transform of C_{n} (k)] are tested against the exact result.

Original language | English (US) |
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Pages (from-to) | 5143-5148 |

Number of pages | 6 |

Journal | The Journal of Chemical Physics |

Volume | 75 |

Issue number | 10 |

Publication status | Published - 1981 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*75*(10), 5143-5148.