GLASS-TRANSITION AND DYNAMIC-MOBILITY SPECTRUM OF AN ISOTROPIC SYSTEMOF RODLIKE MOLECULES

A self-consistent mean-field theory of the glass transition is present ed for the model of a high-density isotropic melt of rodlike molecules , which was originally proposed by Edwards and Evans [J. Chem. Soc. Fa raday Trans. 2 78, 113 (1982)]. In this model, translation along the r od axis is the only mode available, but the diffusional motion of a gi ven rod (hereafter called the test rod) is hindered by end-on collisio ns with the lateral surfaces of other rods that lie in its diffusion p ath. The basis of this treatment is the mean-field Green-function theo ry developed in our previous contribution for one-dimensional diffusio n in the presence of many reflecting barriers [Phys. Rev. A 45, 5426 ( 1992)]. A self-consistency requirement for the dynamics of the test ro d and of the barrier rods leads to an asymptotic decrease to zero in t he long-time diffusion constant, i.e., a glass transition, as the dens ity of the barrier rods exceeds a critical value. The glass transition is manifested in a divergence of the lifetime tau 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, tau follows A rrhenius behavior. A relaxation is observed in the dynamic-mobility sp ectrum of rod translation with a change in the profile between the mob ile and the glassy phases. We also investigate the complex modulus of the melt and find a spectral distribution similar to that for the shea r modulus obtained by reptation theory for entangled linear-chain poly mers.