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The interplay between short-range attractions and long-range repulsions (SALR) characterizes the so called liquids with competing interactions, which are known to exhibit a variety of equilibrium and non-equilibrium phases. The theoretical description of the phenomenology associated to glassy or gel states in these systems has to take into account both, the presence of thermodynamic instabilities (such as those defining the spinodal line and the so called $\lambda$ line) and the limited capability to describe genuine non-equilibrium processes from first principles. Here we report the first application of the non-equilibrium self-consistent generalized Langevin equation theory, to the description of the dynamical arrest processes that occur in SALR systems after being instantaneously quenched into a state point in the regions of thermodynamic instability. The physical scenario predicted by this theory reveals an amazing interplay between the thermodynamically-driven instabilities, favoring equilibrium macro- and micro-phase separation, and the kinetic arrest mechanisms, favoring non-equilibrium amorphous solidification of the liquid into an unexpected variety of glass and gel states.

We report the combined results of molecular dynamics simulations and theoretical calculations concerning various dynamical arrest transitions in a model system representing a dipolar fluid, namely, N (softcore) rigid spheres interacting through a truncated dipole-dipole potential. By exploring different regimes of concentration and temperature, we find three distinct scenarios for the slowing down of the dynamics of the translational and orientational degrees of freedom: At low ({$\eta$} = 0.2) and intermediate (${\eta}$ = 0.4) volume fractions, both dynamics are strongly coupled and become simultaneously arrested upon cooling. At high concentrations ({$\eta$} $\lt$ 0.6), the translational dynamics shows the features of an ordinary glass transition, either by compressing or cooling down the system, but with the orientations remaining ergodic, thus indicating the existence of partially arrested states. In this density regime, but at lower temperatures, the relaxation of the orientational dynamics also freezes. The physical scenario provided by the simulations is discussed and compared against results obtained with the self-consistent generalized Langevin equation theory, and both provide a consistent description of the dynamical arrest transitions in the system. Our results are summarized in an arrested states diagram which qualitatively organizes the simulation data and provides a generic picture of the glass transitions of a dipolar fluid.

The binary hard-sphere mixture is one of the simplest representations of a many-body system with competing time and length scales. This model is relevant to fundamentally understand both the structural and dynamical properties of materials, such as metallic melts, colloids, polymers and bio-based composites. It also allows us to study how different scales influence the physical behavior of a multicomponent glass-forming liquid; a question that still awaits a unified description. In this contribution, we report on distinct dynamical arrest transitions in highly asymmetric binary colloidal mixtures, namely, a single glass of big particles, in which the small species remains ergodic, and a double glass with the simultaneous arrest of both components. When the mixture approaches any glass transition, the relaxation of the collective dynamics of both species becomes coupled. In the single glass domain, spatial modulations occur due to the structure of the large spheres, a feature not observed in the two-glass domain. The relaxation of the \emph{self} dynamics of small and large particles, in contrast, become decoupled at the boundaries of both transitions; the large species always displays dynamical arrest, whereas the small ones appear arrested only in the double glass. Thus, in order to obtain a complete picture of the distinct glassy states, one needs to take into account the dynamics of both species.

A fundamental challenge of the theory of liquids is to understand the similarities and differences in the macroscopic dynamics of both colloidal and atomic liquids, which originate in the (Newtonian or Brownian) nature of the microscopic motion of their constituents. Starting from the recently-discovered long-time dynamic equivalence between a colloidal and an atomic liquid that share the same interparticle pair potential, in this work we develop a self-consistent generalized Langevin equation (SCGLE) theory for the dynamics of equilibrium multicomponent atomic liquids, applicable as an approximate but quantitative theory describing the long-time diffusive dynamical properties of simple equilibrium atomic liquids. When complemented with a Gaussian-like approximation, this theory is also able to provide a reasonable representation of the passage from ballistic to diffusive behavior. We illustrate the applicability of the resulting theory with three particular examples, namely, a monodisperse and a polydisperse monocomponent hard-sphere liquid, and a highly size-asymmetric binary hard-sphere mixture. To assess the quantitative accuracy of our results, we perform event-driven molecular dynamics simulations, which corroborate the general features of the theoretical predictions., Comment: 11 pages, 12 Figures