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

Iwao Teraoka, Frank E. Karasz

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1108-1118
Number of pages11
JournalPhysical Review E
Volume47
Issue number2
DOIs
StatePublished - 1993

Fingerprint

Glass Transition
rods
Molecules
glass
molecules
Modulus
Self-consistency
Spectral Distribution
Mean-field Theory
Mean Field
Critical value
Green's function
Contraction
Lateral
Lifetime
Divergence
Exceed
Power Law
Polymers
Collision

ASJC Scopus subject areas

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

Cite this

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

In: Physical Review E, Vol. 47, No. 2, 1993, p. 1108-1118.

Research output: Contribution to journalArticle

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