Structural relaxation, dynamical arrest, and aging in soft-sphere liquids.

We investigate the structural relaxation of a soft-sphere liquid quenched isochorically (ϕ = 0.7) and instantaneously to different temperatures Tf above and below the glass transition. For this, we combine extensive Brownian dynamics simulations and theoretical calculations based on the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory. The response of the liquid to a quench generally consists of a sub-linear increase of the α-relaxation time with system's age. Approaching the ideal glass-transition temperature from above (Tf > Ta), sub-aging appears as a transient process describing a broad equilibration crossover for quenches to nearly arrested states. This allows us to empirically determine an equilibration timescale teq(Tf) that becomes increasingly longer as Tf approaches Ta. For quenches inside the glass (Tf ≤ Ta), the growth rate of the structural relaxation time becomes progressively larger as Tf decreases and, unlike the equilibration scenario, τα remains evolving within the whole observation time-window. These features are consistently found in theory and simulations with remarkable semi-quantitative agreement and coincide with those revealed in a previous and complementary study [P. Mendoza-Méndez et al., Phys. Rev. 96, 022608 (2017)] that considered a sequence of quenches with fixed final temperature Tf = 0 but increasing ϕ toward the hard-sphere dynamical arrest volume fraction ϕHS a=0.582. The NE-SCGLE analysis, however, unveils various fundamental aspects of the glass transition, involving the abrupt passage from the ordinary equilibration scenario to the persistent aging effects that are characteristic of glass-forming liquids. The theory also explains that, within the time window of any experimental observation, this can only be observed as a continuous crossover.

Magnetic viscoelastic behavior in a colloidal ferrofluid.

Based on the stochastic Langevin equation, we derived the total friction experienced by a tracer particle diffusing in thermally equilibrated colloidal magnetic fluids. This transport property leads to new expressions for its long-time diffusion coefficients, which satisfy an Einstein relation with the frictions of its translational and rotational Brownian motion. Further use of the nano-rheology theory allowed us to derive also the viscoelastic modulus of the colloid from such a property. The temporal relaxation of the viscoelasticity and transport coefficient turns out to be governed by the intermediate scattering function of the colloid. We derived an explicit formula for this evolution function within a hydrodynamic theory to include rotational degrees of freedom of the particles. In the limit of short frequencies, the viscous moduli render a new expression for the static viscosity. We found that its comparison with known experiments, at low and high concentration of ferroparticles in magnetite ferrofluids, is fair. However, comparing the predicted viscoelastic moduli with computer simulations as a function of frequency yields poor agreement.