Nonlinear rheology of dense colloidal systems with short-ranged attraction: A mode-coupling theory analysis

The nonlinear rheology of glass-forming colloidal suspensions with short-ranged attractions is discussed within the integration-through transients framework combined with the mode-coupling theory of the glass transition (ITT-MCT). Calculations are based on the square-well system (SWS), as a model for colloid-polymer mixtures. The high-density regime featuring reentrant melting of the glass upon increasing the attraction strength, and the crossover from repulsive glasses formed at weak attraction to attractive glasses formed at strong attraction, are discussed. Flow curves are found in qualitative agreement with experimental data, featuring a strong increase in the yield stress, and, for suitable interaction parameters, the crossover between two yield stresses. The yield strain, defined as the position of the stress overshoot under startup flow, is found to be proportional to the attraction range for strong attraction. At weak and intermediate attraction strength, the combined effects of hard-core caging and attraction-driven bonding result in a richer dependence on the parameters. The first normal-stress difference exhibits a weaker dependence on short-ranged attractions as the shear stress, since the latter is more sensitive the short-wavelength features of the static structure.Comment: 14 pages, 12 figure

How Glassy Relaxation Slows Down by Increasing Mobility

We investigate how structural relaxation in mixtures with strong dynamical asymmetry is affected by the microscopic dynamics. Brownian and Newtonian dynamics simulations of dense mixtures of fast and slow hard spheres reveal a striking trend reversal. Below a critical density, increasing the mobility of the fast particles fluidizes the system, yet, above that critical density, the same increase in mobility strongly hinders the relaxation of the slow particles. The critical density itself does not depend on the dynamical asymmetry and can be identified with the glass-transition density of the mode-coupling theory. The asymptotic dynamics close to the critical density is universal, but strong pre-asymptotic effects prevail in mixtures with additional size asymmetry. This observation reconciles earlier findings of a strong dependence on kinetic parameters of glassy dynamics in colloid--polymer mixtures with the paradigm that the glass transition is determined by the properties of configuration space alone

Mode-Coupling Theory for Active Brownian Particles

We present a mode-coupling theory (MCT) for the high-density dynamics of two-dimensional spherical active Brownian particles (ABP). The theory is based on the integration-through-transients (ITT) formalism and hence provides a starting point for the calculation of non-equilibrium averages in active-Brownian particle systems. The ABP are characterized by a self-propulsion velocity $v_0$, and by their translational and rotational diffusion coefficients, $D_t$ and $D_r$. The theory treats both the translational and the orientational degrees of freedom of ABP explicitly. This allows to study the effect of self-propulsion of both weak and strong persistence of the swimming direction, also at high densities where the persistence length $\ell_p=v_0/D_r$ is large compared to the typical interaction length scale. While the low-density dynamics of ABP is characterized by a single P\'eclet number, $Pe=v_0^2/D_rD_t$, close to the glass transition the dynamics is found to depend on $Pe$ and $\ell_p$ separately. At fixed density, increasing the self-propulsion velocity causes structural relaxatino to speed up, while decreasing the persistence length slows down the relaxation. The theory predicts a non-trivial idealized-glass-transition diagram in the three-dimensional parameter space of density, self-propulsion velocity and rotational diffusivity. The active-MCT glass is a nonergodic state where correlations of initial density fluctuations never fully decay, but also an infinite memory of initial orientational fluctuations is retained in the positions

Localization phenomena in models of ion-conducting glass formers

The mass transport in soft-sphere mixtures of small and big particles as well as in the disordered Lorentz gas (LG) model is studied using molecular dynamics (MD) computer simulations. The soft-sphere mixture shows anomalous small-particle diffusion signifying a localization transition separate from the big-particle glass transition. Switching off small-particle excluded volume constraints slows down the small-particle dynamics, as indicated by incoherent intermediate scattering functions. A comparison of logarithmic time derivatives of the mean-squared displacements reveals qualitative similarities between the localization transition in the soft-sphere mixture and its counterpart in the LG. Nevertheless, qualitative differences emphasize the need for further research elucidating the connection between both models.Comment: to appear in Eur. Phys. J. Special Topic

Qualitative Features at the Glass Crossover

We discuss some generic features of the dynamics of glass-forming liquids close to the glass transition singularity of the idealized mode-coupling theory (MCT). The analysis is based on a recent model by one of the authors for the intermediate-time dynamics ($\beta$ relaxation), derived by applying dynamical field-theory techniques to the idealized MCT. Combined with the assumption of time-temperature superposition for the slow structural ($\alpha$) relaxation, the model naturally explains three prominent features of the dynamical crossover: the change from a power-law to exponential increase in the structural relaxation time, the replacement of the Stokes-Einstein relation between diffusion and viscosity by a fractional law, and two distinct growth regimes of the thermal susceptibility that has been associated to dynamical heterogeneities

Scaling equations for mode-coupling theories with multiple decay channels

Multiple relaxation channels often arise in the dynamics of liquids where the momentum current associated to the particle-conservation law splits into distinct contributions. Examples are strongly confined liquids for which the currents in lateral and longitudinal direction to the walls are very different, or fluids of nonspherical particles with distinct relaxation patterns for translational and rotational degrees of freedom. Here, we perform an asymptotic analysis of the slow structural relaxation close to kinetic arrest as described by mode-coupling theory (MCT) with several relaxation channels. Compared to standard MCT, the presence of multiple relaxation channels significantly changes the structure of the underlying equations of motion and leads to additional, non-trivial terms in the asymptotic solution. We show that the solution can be rescaled, and thus prove that the well-known $\beta$-scaling equation of MCT remains valid even in the presence of multiple relaxation channels. The asymptotic treatment is validated using a novel schematic model. We demonstrate that the numerical solution of this schematic model can indeed be described by the derived asymptotic scaling laws close to kinetic arrest. Additionally, clear traces of the existence of two distinct decay channels are found in the low-frequency susceptibility spectrum, suggesting that clear footprints of the additional relaxation channels can in principle be detected in simulations or experiments of confined or molecular liquids.Comment: Accepted by J. Stat. Mech.: Theory and Experiments, https://iopscience.iop.org/journal/1742-546