Random-walk analysis of displacement statistics of particles in concentrated suspensions of hard spheres

Interplay of adsorption and surface mobility in tracer diffusion in porous media

We model the diffusion of a tracer that interacts with the internal surface of a porous medium formed by a packing of solid spheres. The tracer executes a lattice random walk in which hops from surface to bulk sites and hops on the surface have small probabilities compared to hops from bulk sites; those probabilities are related to bulk and surface diffusion coefficients and to a desorption rate. A scaling approach distinguishes three regimes of steady state diffusion, which are confirmed by numerical simulations. If the product of desorption rate and sphere diameter is large, dominant bulk residence is observed and the diffusion coefficient is close to the bulk value. If that product is small and the surface mobility is low, the tracers are adsorbed most of the time but most hops are executed in the bulk. However, for high surface mobility, there is a nontrivial regime of dominant surface displacement, since the connectivity of solid walls allows the tracers to migrate to long distances while they are adsorbed. In this regime, we observe rounded tracer paths on the sphere walls, which are qualitatively similar to those of a recent experiment on polystyrene particle diffusion. The calculated average residence times are proportional to the bulk and surface densities of an equilibrium ensemble of noninteracting tracers, and the relation between those densities sets the adsorption isotherm. Simulations performed with initially uniform (nonequilibrium) distribution of tracers in the pores show other nontrivial results in cases of dominant surface residence: slow increase of the mean-square displacement at short times, since the tracer has not explored a homogeneous medium, and a remarkable slowdown between the first encounter with a solid wall and the first hop from that point. Relations between our results and other models of diffusion and adsorption in porous media are discussed.

Slow dynamics and aging of a colloidal hard sphere glass

The intermediate scattering function (ISF) is measured for a colloidal hard-sphere glass as functions of the scattering vector and waiting time. For scattering vectors near the structure factor peak, we show that the ISF and the stretching index, defined at the crossover time between the fast and slow processes, depend algebraically on the waiting time. By contrast, the Debye-Waller factor is independent of the waiting time.

Dynamical heterogeneity and the freezing transition in hard-sphere suspensions: further analysis of the mean square displacement and the velocity autocorrelation function

The velocity autocorrelation function is derived from the mean-squared displacement measured on a colloidal suspension of particles with hard-sphere-like interactions. It decays to zero from below and follows a stretched exponential function of delay time for the thermodynamically stable suspension. For the metastable suspension a power-law decay emerges. The results are discussed in terms of the classical Lorentz gas and the model that describes diffusion confined to one dimension. With the aid of these models, the experimental results provide a characterization of the dynamical heterogeneities which are observed microscopically, and an explanation for the enhanced resistance to flow and diffusion usually found in undercooled fluids upon approaching the glass transition.

Dynamical perspective of the freezing transition of a suspension of hard spheres from the velocity autocorrelation function

The velocity autocorrelation function of concentrated colloidal fluids of hard-sphere particles, measured by dynamic light scattering, decays to the experimental noise floor from below. The decay follows a stretched exponential function of delay time for the colloidal fluid in thermodynamic equilibrium, and a power law for the nonequilibrium, undercooled colloidal fluid. Consideration of this difference between the two states points to a possible dynamical mechanism of freezing.