Glassy dynamics in asymmetric binary mixtures of hard spheres.

We perform a systematic and detailed study of the glass transition in highly asymmetric binary mixtures of colloidal hard spheres, combining differential dynamic microscopy experiments, event-driven molecular dynamics simulations, and theoretical calculations, exploring the whole state diagram and determining the self-dynamics and collective dynamics of both species. Two distinct glassy states involving different dynamical arrest transitions are consistently described, namely, a double glass with the simultaneous arrest of the self-dynamics and collective dynamics of both species, and a single glass of large particles in which the self-dynamics of the small species remains ergodic. In the single-glass scenario, spatial modulations in the collective dynamics of both species occur due to the structure of the large spheres, a feature not observed in the double-glass domain. The theoretical results, obtained within the self-consistent generalized Langevin equation formalism, are in agreement with both simulations and experimental data, thus providing a stringent validation of this theoretical framework in the description of dynamical arrest in highly asymmetric mixtures. Our findings are summarized in a state diagram that classifies the various amorphous states of highly asymmetric mixtures by their dynamical arrest mechanisms.

Assessment of the micro-structure and depletion potentials in two-dimensional binary mixtures of additive hard-disks.

Depletion forces are a particular class of effective interactions that have been mainly investigated in binary mixtures of hard-spheres in bulk. Although there are a few contributions that point toward the effects of confinement on the depletion potential, little is known about such entropic potentials in two-dimensional colloidal systems. From theoretical point of view, the problem resides in the fact that there is no general formulation of depletion forces in arbitrary dimensions and, typically, any approach that works well in three dimensions has to be reformulated for lower dimensionality. However, we have proposed a theoretical framework, based on the formalism of contraction of the description within the integral equations theory of simple liquids, to account for effective interactions in colloidal liquids, whose main feature is that it does not need to be readapted to the problem under consideration. We have also shown that such an approach allows one to determine the depletion pair potential in three-dimensional colloidal mixtures even near to the demixing transition, provided the bridge functions are sufficiently accurate to correctly describe the spatial correlation between colloids [E. López-Sánchez et al., J. Chem. Phys. 139, 104908 (2013)]. We here report an extensive analysis of the structure and the entropic potentials in binary mixtures of additive hard-disks. In particular, we show that the same functional form of the modified-Verlet closure relation used in three dimensions can be straightforwardly employed to obtain an accurate solution for two-dimensional colloidal mixtures in a wide range of packing fractions, molar fractions, and size asymmetries. Our theoretical results are explicitly compared with the ones obtained by means of event-driven molecular dynamics simulations and recent experimental results. Furthermore, to assess the accuracy of our predictions, the depletion potentials are used in an effective one-component model to reproduce the structure of either the big or the small disks. This demonstrates the robustness of our theoretical scheme even in two dimensions.