Mode-coupling Theory Of Glass Transition Research Articles

Mode-Coupling theory for glass transition of active-passive binary mixture

Collective behaviours of active particle systems have gained great research attentions in recent years. Here we present a mode-coupling theory (MCT) framework to study the glass transition of a mixture system of active and passive Brownian particles. The starting point is an effective Smoluchowski equation, which governs the dynamics of the probability distribution function in the position phase space. With the assumption of the existence of a nonequilibrium steady state, we are able to obtain dynamic equations for the intermediate scattering functions (ISFs), wherein an irreducible memory function is introduced which in turn can be written as functions of the ISFs based on standard mode-coupling approximations. The effect of particle activity is included through an effective diffusion coefficient which can be obtained via short time simulations. By calculating the long-time limit of the ISF, the Debye-Waller (DW) factor, one can determine the critical packing fraction ηc of glass transition. We find that for active-passive (AP) mixtures with the same particle sizes, ηc increases as the partial fraction of active particle xA increases, which is in agreement with previous simulation works. For system with different active/passive particle sizes, we find an interesting reentrance behaviour of glass transition, i.e., ηc shows a non-monotonic dependence on xA. In addition, such a reentrance behaviour would disappear if the particle activity is large enough. Our results thus provide a useful theoretical scheme to study glass transition behaviour of active-passive mixture systems in a promising way.

A possible scenario for the fragile-to-strong dynamic crossover predicted by the extendedmode-coupling theory for glass transition

It is argued that the extended mode-coupling theory for glass transition predicts a dynamic crossover inthe α-relaxation time and in the self-diffusion constant as a general implication of the structureof its equations of motion. This crossover occurs near the critical temperatureTc of the idealized version of the theory, and is caused by the change in the dynamics from the onedetermined by the cage effect to that dominated by hopping processes. When combined with amodel for the hopping kernel deduced from the dynamical theory for diffusion–jump processes,the dynamic crossover can be identified as the fragile-to-strong crossover (FSC) in which theα-relaxation time and the self-diffusion constant cross over from a non-Arrhenius to anArrhenius behavior. Since the present theory does not resort to the existence of theso-called Widom line, to which the FSC in confined water has been attributed, it provides apossible explanation of the FSC observed in a variety of glass-forming systems in which theexistence of the Widom line is unlikely. In addition, the present theory predicts that theStokes–Einstein relation (SER) breaks down in different ways on the fragile and strongsides of the FSC, in agreement with the experimental observation in confined water. It isalso demonstrated that the violation of the SER in both the fragile and strong regions canbe fitted reasonably well by a single fractional relation with an empirical exponent of 0.85.

On the applicability of the mode-coupling theory of glass transitions to good glass formers

Qualitative features of the predictions of the mode-coupling theory of glass transition are compared with the observed behaviour of good glass formers. In particular, the validity of the idealisation of a sharp glass transitions, which is independent of the rate of cooling, is examined critically. A possible extension of the theory is indicated, by which the variability of glass structure on changing the conditions of cooling could be taken into account.