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

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.