### Abstract

A self-consistent mean-field theory of the glass transition is presented for the model of a high-density isotropic melt of rodlike molecules, which was originally proposed by Edwards and Evans [J. Chem. Soc. Faraday Trans. 2 78, 113 (1982)]. In this model, translation along the rod axis is the only mode available, but the diffusional motion of a given rod (hereafter called the test rod) is hindered by end-on collisions with the lateral surfaces of other rods that lie in its diffusion path. The basis of this treatment is the mean-field Green-function theory developed in our previous contribution for one-dimensional diffusion in the presence of many reflecting barriers [Phys. Rev. A 45, 5426 (1992)]. A self-consistency requirement for the dynamics of the test rod and of the barrier rods leads to an asymptotic decrease to zero in the long-time diffusion constant, i.e., a glass transition, as the density of the barrier rods exceeds a critical value. The glass transition is manifested in a divergence of the lifetime of the barrier in a power-law (T-T1)-2 relation as the temperature T approaches a glass-transition temperature T1 from above if a linear thermal contraction is assumed in the mobile phase. At a higher temperature, follows Arrhenius behavior. A relaxation is observed in the dynamic-mobility spectrum of rod translation with a change in the profile between the mobile and the glassy phases. We also investigate the complex modulus of the melt and find a spectral distribution similar to that for the shear modulus obtained by reptation theory for entangled linear-chain polymers.

Original language | English (US) |
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Pages (from-to) | 1108-1118 |

Number of pages | 11 |

Journal | Physical Review E |

Volume | 47 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1993 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E*,

*47*(2), 1108-1118. https://doi.org/10.1103/PhysRevE.47.1108