Dynamical model of the liquid-glass transition

Abstract

Based on a microscopic theory developed recently, a dynamical model of density fluctuations in simple fluids and glasses is proposed and analyzed analytically and numerically. The model exhibits a liquid-glass transition, where the glassy phase is characterized by a zero-frequency pole of the longitudinal and transverse viscosities indicating the systems' stability against stress. This also implies an elastic peak in the density-fluctuation spectrum. Approaching the glass transition the slowing down of density fluctuations is controlled by the increasing longitudinal viscosity, which in turn is coupled via a nonlinear feedback mechanism to the slowly decaying density fluctuations. This causes a divergence of the structural relaxation time at a certain critical coupling constant ${\ensuremath{\lambda}}_{c}$. At the glass transition density fluctuations decay with a long-time power law $\ensuremath{\Phi}(t)\ensuremath{\sim}{t}^{\ensuremath{-}\ensuremath{\alpha}}$ with $\ensuremath{\alpha}=0.395$ and approaching the transition the viscosity diverges proportional to ${\ensuremath{\epsilon}}^{\ensuremath{-}\ensuremath{\mu}}$ and ${\ensuremath{\epsilon}}^{\ensuremath{-}\ensuremath{\mu}}$, where $\ensuremath{\epsilon}=|1\ensuremath{-}\frac{\ensuremath{\lambda}}{{\ensuremath{\lambda}}_{c}}|$ and $\ensuremath{\mu}=\frac{(1+\ensuremath{\alpha})}{2\ensuremath{\alpha}}$, ${\ensuremath{\mu}}^{\ensuremath{'}}=\ensuremath{\mu}\ensuremath{-}1$ below and above the transition, respectively. The long-time tail "paradox" in dense fluids is briefly discussed.