Glass transition and self-consistent mode-coupling theory

The implications of a self-consistent mode-coupling theory of dense fluids for the liquid-glass transition are considered. First, we show that when higher-order corrections are ignored from our model, there is a dynamic transition of the hard-sphere fluid at an intermediate density to an ideal glassy phase. This is in agreement with earlier theoretical works. Next, we demonstrate that in the present model there is a cutoff mechanism that rounds off the sharp transition. We compute the transport coefficients for the hard-sphere fluid, which show good agreement with computer-simulation results at supercooled densities. The viscosity follows a power-law increase for the intermediate densities with an exponent close to 2. For very high densities the sharp transition is cut off and the transport coefficient increases at a slower rate. We calculate how the density autocorrelation function in a Lennard-Jones fluid decays in time. This is done for different densities along an isotherm. Our results agree much better with the slow relaxation observed in molecular-dynamics simulations than earlier theories.