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Modecoupling Theory for Glass Transition of Activepassive Binary Mixture 
Zhonghuai Hou



Abstract: 
Collective behaviours of active particle systems have gained great research attentions in recent
years. Here we present a modecoupling theory (MCT) framework to study the glass transition
of a mixture system of active and passive Brownian particles. The starting point is an eective
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 modecoupling approximations. The eect of particle activity is included through
an eective diusion coecient which can be obtained via short time simulations. By calculating
the longtime limit of the ISF, the DebyeWaller (DW) factor, one can determine the critical packing
fraction c of glass transition. We nd that for activepassive (AP) mixtures with the same particle
sizes, c increases as the partial fraction xA of active particle increases which is in agreement
with previous simulation works. For system with dierent active/passive particle sizes, we nd
an interesting reentrance behaviour of glass transition, i.e., c shows a nonmonotonic 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
activepassive mixture systems in a promising way. 
Key words: glass transition, modecoupling theory, active particles, activepassive particle mixture 
FundProject: 

Modecoupling Theory for Glass Transition of Activepassive Binary Mixture 
Z. Hou

摘要: 
Collective behaviours of active particle systems have gained great research attentions in recent
years. Here we present a modecoupling theory (MCT) framework to study the glass transition
of a mixture system of active and passive Brownian particles. The starting point is an eective
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 modecoupling approximations. The eect of particle activity is included through
an eective diusion coecient which can be obtained via short time simulations. By calculating
the longtime limit of the ISF, the DebyeWaller (DW) factor, one can determine the critical packing
fraction c of glass transition. We nd that for activepassive (AP) mixtures with the same particle
sizes, c increases as the partial fraction xA of active particle increases which is in agreement
with previous simulation works. For system with dierent active/passive particle sizes, we nd
an interesting reentrance behaviour of glass transition, i.e., c shows a nonmonotonic 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
activepassive mixture systems in a promising way. 
关键词: glass transition, modecoupling theory, active particles, activepassive particle mixture 
DOI： 
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