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Register a new userProbability densities of a forced probe particle in glass: results from mode coupling theory and simulations of active microrheology
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We investigate the displacements of a probe particle inside a glass, when a strong external force is applied to the probe (active nonlinear microrheology). Calculations within mode coupling theory are presented for glasses of hard spheres and compared to Langevin and Brownian dynamics simulations. Under not too strong forces where the probe remains trapped, the probe density distribution becomes anisotropic. It is shifted towards the direction of the force, develops an enhanced tail in that direction (signalled by a positive skewness), and exhibits different variances along and perpendicular to the force direction. A simple model of an harmonically trapped probe rationalizes the low force limit, with strong strain softening setting in at forces of the order of a few thermal energies per particle radius.
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The glass transition remains unclarified in condensed matter physics. Investigating the mechanical properties of glass is challenging because any global deformation that may result in shear rejuvenation requires an astronomical relaxation time. Moreover, it is well known that a glass is heterogeneous and a global perturbation cannot explore local mechanical/transport properties. However, an investigation based on a local probe, i.e. microrheology, may overcome these problems. Here, we establish active microrheology of a bulk metallic glass: a probe particle driven into host medium glass. This is a technique amenable for experimental investigations. We show that upon cooling the microscopic friction exhibits a second-order phase transition; this sheds light on the origin of friction in heterogeneous materials. Further, we provide distinct evidence to demonstrate that a strong relationship exists between the microscopic dynamics of the probe particle and the macroscopic properties of the host medium glass. These findings establish active microrheology as a promising technique for investigating the local properties of bulk metallic glass.
We discuss recent advances in developing a mode-coupling theory of the glass transition (MCT) of two-dimensional systems of active Brownian particles (ABP). 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. 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 (ITT) 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.
In the technique of microrheology, macroscopic rheological parameters as well as information about local structure are deduced from the behavior of microscopic probe particles under thermal or active forcing. Microrheology requires knowledge of the relation between macroscopic parameters and the force felt by a particle in response to displacements. We investigate this response function for a spherical particle using the two-fluid model, in which the gel is represented by a polymer network coupled to a surrounding solvent via a drag force. We obtain an analytic solution for the response function in the limit of small volume fraction of the polymer network, and neglecting inertial effects. We use no-slip boundary conditions for the solvent at the surface of the sphere. The boundary condition for the network at the surface of the sphere is a kinetic friction law, for which the tangential stress of the network is proportional to relative velocity of the network and the sphere. This boundary condition encompasses both no-slip and frictionless boundary conditions as limits. Far from the sphere there is no relative motion between the solvent and network due to the coupling between them. However, the different boundary conditions on the solvent and network tend to produce different far-field motions. We show that the far field motion and the force on the sphere are controlled by the solvent boundary conditions at high frequency and by the network boundary conditions at low frequency. At low frequencies compression of the network can also affect the force on the sphere. We find the crossover frequencies at which the effects of sliding of the sphere past the polymer network and compression of the gel become important.
We derive a mode-coupling theory (MCT) to describe the dynamics of tracer particles in dense systems of active Brownian particles (ABPs) in two spatial dimensions. The ABP undergo translational and rotational Brownian dynamics, and are equipped with a fixed self-propulsion speed along their orientational vector that describes their active motility. The resulting equations of motion for the tagged-particle density correlation functions describe the various cases of tracer dynamics close to the glass transition: that of a passive colloidal particle in a suspension of ABP, that of a single active particle in a glass-forming passive host suspensions, and that of active tracers in a bath of active particles. Numerical results are presented for these cases assuming hard-sphere interactions among the particles. The qualitative and quantitative accuracy of the theory is tested against event-driven Brownian dynamics (ED-BD) simulations of active and passive hard disks. Simulation and theory are found in quantitative agreement, provided one adjusts the overall density (as known from the passive description of glassy dynamics), and allows for a rescaling of self-propulsion velocities in the active host system. These adjustments account for the fact that ABP-MCT generally overestimates the tendency for kinetic arrest. We also confirm in the simulations a peculiar feature of the transient and stationary dynamical density correlation functions regarding their lack of symmetry under time reversal, demonstrating the non-equilibrium nature of the system and how it manifests itself in the theory.
Understanding the physics of glass formation remains one of the major unsolved challenges of condensed matter science. As a material solidifies into a glass, it exhibits a spectacular slowdown of the dynamics upon cooling or compression, but at the same time undergoes only minute structural changes. Among the numerous theories put forward to rationalize this complex behavior, Mode-Coupling Theory (MCT) stands out as the only framework that provides a fully first-principles-based description of glass phenomenology. This review outlines the key physical ingredients of MCT, its predictions, successes, and failures, as well as recent improvements of the theory. We also discuss the extension and application of MCT to the emerging field of non-equilibrium active soft matter
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