The European Physical Journal E ( IF 1.8 ) Pub Date : 2021-03-11 , DOI: 10.1140/epje/s10189-021-00039-4 Julian Reichert 1 , Leon F Granz 1 , Thomas Voigtmann 1, 2
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Abstract
We discuss recent advances in developing a mode-coupling theory of the glass transition (MCT) of two-dimensional systems of active Brownian particles (ABPs). The theory describes the structural relaxation close to the active glass in terms of transient dynamical density correlation functions. We summarize the equations of motion that have been derived for the collective density-fluctuation dynamics and those for the tagged-particle motion. The latter allow to study the dynamics of both passive and active tracers in both passive and active host systems. In the limit of small wave numbers, they give rise to equations of motion describing the mean-squared displacements (MSDs) of these tracers and hence the long-time diffusion coefficients as a transport coefficient quantifying long-range tracer motion. We specifically discuss the case of a single ABP tracer in a glass-forming passive host suspension, a case that has recently been studied in experiments on colloidal Janus particles. We employ event-driven Brownian dynamics (ED-BD) computer simulations to test the ABP-MCT and find good agreement between the two for the MSD, provided that known errors in MCT already for the passive system (i.e., an overestimation of the glassiness of the system) are accounted for by an empirical mapping of packing fractions and host-system self-propulsion forces. The ED-BD simulation results also compare well to experimental data, although a peculiar non-monotonic mapping of self-propulsion velocities is required. The ABP-MCT predicts a specific self-propulsion dependence of the Stokes–Einstein relation between the long-time diffusion coefficient and the host-system viscosity that matches well the results from simulation. An application of ABP-MCT within the integration-through transients framework to calculate the density-renormalized effective swim velocity of the interacting ABP agrees qualitatively with the ED-BD simulation data at densities close to the glass transition and quantitatively for the full density range only after the mapping of packing fractions employed for the passive system.
Graphic abstract
中文翻译：
致密活性布朗粒子系统中的输运系数：模式耦合理论和模拟结果
抽象的
我们讨论了活性布朗粒子（ABP）二维系统玻璃化转变（MCT）模式耦合理论的最新进展。该理论用瞬态动态密度相关函数描述了接近活性玻璃的结构弛豫。我们总结了集体密度涨落动力学和标记粒子运动的运动方程。后者允许研究被动和主动主机系统中被动和主动示踪剂的动态。在小波数的限制下，它们产生了描述这些示踪剂的均方位移（MSD）的运动方程，因此产生了作为量化长程示踪剂运动的传输系数的长时间扩散系数。我们特别讨论了玻璃形成被动主体悬浮液中单个 ABP 示踪剂的情况，最近在胶体 Janus 颗粒实验中研究了这种情况。我们采用事件驱动布朗动力学 (ED-BD) 计算机模拟来测试 ABP-MCT，并在 MSD 的两者之间找到良好的一致性，前提是被动系统的 MCT 中已经存在已知误差（即，高估了玻璃度）系统的）由堆积分数和主机系统自推进力的经验映射来解释。尽管需要特殊的自推进速度非单调映射，但 ED-BD 模拟结果也与实验数据进行了很好的比较。 ABP-MCT 预测了长期扩散系数和主系统粘度之间斯托克斯-爱因斯坦关系的特定自推进依赖性，这与模拟结果很好地匹配。 在瞬态积分框架内应用 ABP-MCT 来计算相互作用的 ABP 的密度重整化有效游动速度，在接近玻璃化转变的密度下与 ED-BD 模拟数据定性一致，并且仅在整个密度范围内定量一致在绘制用于无源系统的填充分数之后。
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