Glass–liquid–glass reentrance in mono-component colloidal dispersions

Abstract

The self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics isemployed to describe the ergodic–non-ergodic transition in model mono-disperse colloidaldispersions whose particles interact through hard-sphere plus short-ranged attractive forces.The ergodic–non-ergodic phase diagram in the temperature–concentration state space isdetermined for the hard-sphere plus attractive Yukawa model within the meanspherical approximation for the static structure factor by solving a remarkably simpleequation for the localization length of the colloidal particles. Finite real values ofthis property signals non-ergodicity and determines the non-ergodic parametersf(k) and fs(k). The resulting phase diagram for this system, which involves the existence of reentrant(repulsive and attractive) glass states, is compared with the corresponding prediction ofmode coupling theory. Although both theories coincide in the general features of this phasediagram, there are also clear qualitative differences. One of the most relevant is the SCGLEprediction that the ergodic–attractive glass transition does not preempt the gas–liquidphase transition, but always intersects the corresponding spinodal curve on itshigh-concentration side. We also calculate the ergodic–non-ergodic phase diagram for thesticky hard-sphere model to illustrate the dependence of the predicted SCGLE dynamicphase diagram on the choice of one important constituent element of the SCGLE theory.