### 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) |
---|---|

Pages (from-to) | 1108-1118 |

Number of pages | 11 |

Journal | Physical Review E |

Volume | 47 |

Issue number | 2 |

DOIs | |

State | Published - 1993 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E*,

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

**Glass transition and dynamic-mobility spectrum of an isotropic system of rodlike molecules.** / Teraoka, Iwao; Karasz, Frank E.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 47, no. 2, pp. 1108-1118. https://doi.org/10.1103/PhysRevE.47.1108

}

TY - JOUR

T1 - Glass transition and dynamic-mobility spectrum of an isotropic system of rodlike molecules

AU - Teraoka, Iwao

AU - Karasz, Frank E.

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=35949006210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35949006210&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.47.1108

DO - 10.1103/PhysRevE.47.1108

M3 - Article

AN - SCOPUS:35949006210

VL - 47

SP - 1108

EP - 1118

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 2

ER -