摘要
Collective behaviours of active particle systems have gained great research attentions in re- cent 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 eff）ctive Smoluchowski equation, which governs the dynamics of the probability dis- tribution 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 difIusion 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.
基金
supported by the Ministry of Science and Technology of China(No.2016YFA0400904and No.2013CB834606)
the National Natural Science Foundation of China(No.21673212,No.21521001,No.21473165,No.21403204)
the Fundamental Research Funds for the Central Universities(No.WK2030020028 and No.2340000074)
