Metastability, Mode Coupling and the Glass Transition

Mode coupling theory (MCT) has been successful in explaining the observed sequence of time relaxations in dense fluids. Previous expositions of this theory showing this sequence have required the existence of an ideal glass transition temperature $T_0$. Recent experiments show no evidence of $T_0$. We show here how the theory can be reformulated, in a fundamental way, such that one retains this sequence of relaxation behaviors but with a smooth temperature dependence and without any indication of $T_0$. The key ingredient in the reformulation is the inclusion of the metastable nature of the glass transition problem through a coupling of the mass density to the defect density. A main result of our theory is that the exponents governing the sequence of time relaxations are weak functions of the temperature in contrast to the results from conventional MCT.Comment: 14 pages (2 figures upon request), REVTEX

Metastable Dynamics above the Glass Transition

The element of metastability is incorporated in the fluctuating nonlinear hydrodynamic description of the mode coupling theory (MCT) of the liquid-glass transition. This is achieved through the introduction of the defect density variable $n$ into the set of slow variables with the mass density $\rho$ and the momentum density ${\bf g}$. As a first approximation, we consider the case where motions associated with $n$ are much slower than those associated with $\rho$. Self-consistently, assuming one is near a critical surface in the MCT sense, we find that the observed slowing down of the dynamics corresponds to a certain limit of a very shallow metastable well and a weak coupling between $\rho$ and $n$. The metastability parameters as well as the exponents describing the observed sequence of time relaxations are given as smooth functions of the temperature without any evidence for a special temperature. We then investigate the case where the defect dynamics is included. We find that the slowing down of the dynamics corresponds to the system arranging itself such that the kinetic coefficient $\gamma_v$ governing the diffusion of the defects approaches from above a small temperature-dependent value $\gamma^c_v$.Comment: 38 pages, 14 figures (6 figs. are included as a uuencoded tar- compressed file. The rest is available upon request.), RevTEX3.0+eps