Ergodicity–nonergodicity transition in a binary mixture: role of the adiabatic approximation

Abstract

The mode coupling theory (MCT) for glassy dynamics, in its simplest form, predicts an ergodicity–nonergodicity (ENE) transition in a binary mixture beyond a critical packing fraction ηc. The ENE transition is characterized in terms of the so called nonergodicity-parameters (NEP) which are long time limits of the respective set of density-correlation functions for the mixture. The NEP’s remain zero in the ergodic liquid state and jump to respective nonzero values at ηc. We demonstrate here that this discontinuous jump of the NEP’s which is typical in MCT, changes to continuous growth for a binary mixture having large disparities in mass and sizes of its two constituent species. The NEP’s are obtained as respective solutions of a set of nonlinear integral equations, which follow from the equations of fluctuating nonlinear hydrodynamics (FNH). These FNH equations are based on appropriate conservation laws for the two component system. The nonlocal and nonlinear effects of hydrodynamic fluctuations at high density are considered here in the so called adiabatic approximation which assumes fast relaxation of fluctuations in momentum-density compared to that of number-density. The NEP’s behaviours are analysed with using both static and dynamic approaches and they are found to be in agreement.