Kinetic lattice-gas model of cage effects in high-density liquids and a test of mode-coupling theory of the ideal-glass transition

Abstract

We have devised a kinetic lattice-gas model of an atomic liquid that incorporates the physical features associated with the formation of cages around a particle at high density. The model has simple equilibrium statistics, with a maximum of one particle per lattice site, and simple dynamical rules, so that it is feasible to perform dynamical calculations of the fluctuations about equilibrium over very long time scales. The cages inhibit the motion of the particles and cause the self-diffusion coefficient to fall rapidly with increasing density. Simulation results indicate that as the density \ensuremath{\rho}, defined as the number of particles per lattice site, approaches 0.881, the self-diffusion constant behaves in a critical way as (0.881-\ensuremath{\rho}${)}^{3.2}$. The time dependence of density-density correlation functions is calculated from the simulation results, and relaxation times extracted from these functions show a similar critical behavior. These results suggest that the model undergoes a dynamical transition from ergodic to nonergodic behavior. By investigating different system sizes we exclude the possibility that the observed transition is just a finite-size effect related to the bootstrap percolation problem. The mode-coupling theory (MCT) of ergodic-nonergodic transitions in the absence of activated hopping processes is tested for this model by comparing the behavior of the density correlation functions with the predictions of MCT. Surprisingly few of the MCT predictions hold for the system, depsite the fact that the model was devised to incorporate, in a schematic way, the dynamical cage effects that the MCT is usually regarded as describing. Thus the MCT does not provide a correct description of the cage-induced ideal-glass transition of this model.