Universal self-diffusion and subdiffusion in colloids at freezing

Simple liquids' quasiuniversality and the hard-sphere paradigm

This topical review discusses the quasiuniversality of simple liquids' structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field.

Brownian particles on rough substrates: relation between intermediate subdiffusion and asymptotic long-time diffusion

Brownian particles in random potentials show an extended regime of subdiffusive dynamics at intermediate times. The asymptotic diffusive behavior is often established at very long times and thus cannot be accessed in experiments or simulations. For the case of one-dimensional random potentials with Gaussian distributed energies, we present a detailed analysis of experimental and simulation data. It is shown that the asymptotic long-time diffusion coefficient can be related to the behavior at intermediate times, namely, the minimum of the exponent that characterizes subdiffusion and hence corresponds to the maximum degree of subdiffusion. As a consequence, investigating only the dynamics at intermediate times is sufficient to predict the order of magnitude of the long-time diffusion coefficient and the time scale at which the crossover from subdiffusion to diffusion occurs, i.e., when the long-time diffusive regime and hence thermal equilibrium is established. Inversely, theoretical predictions derived for the asymptotic long-time behavior can be used to quantitatively characterize the intermediate behavior, which hardly has been studied so far.

NVU perspective on simple liquids' quasiuniversality

The last half-century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy hypersurfaces constitute a quasiuniversal family of compact Riemannian manifolds parametrized by a single number; from this follows the quasiuniversalities.

Brownian particles in random and quasicrystalline potentials: how they approach the equilibrium

We study the Brownian motion of an ensemble of single colloidal particles in a random square and a quasicrystalline potential when they start from non-equlibrium. For both potentials, Brownian dynamics simulations reveal a widespread subdiffusive regime before the diffusive long-time limit is reached in thermal equilibrium. We develop a random trap model based on a distribution for the depths of trapping sites that reproduces the results of the simulations in detail. Especially, it gives analytic formulas for the long-time diffusion constant and the relaxation time into the diffusive regime. Aside from detailed differences, our work demonstrates that quasicrystalline potentials can be used to mimic aspects of random potentials.

Adsorption and diffusion of molecular nitrogen in single wall carbon nanotubes

Using molecular simulation, the adsorption and self-diffusion of diatomic nitrogen molecules inside a single wall carbon nanotube have been studied over a range of nanotube diameters (8.61-15.66 A) and loadings at temperatures of 100 and 298 K. Nitrogen adsorption energy is found to increase as the nanotube diameter is reduced toward the molecular diameter of nitrogen. A discrete organization of the nitrogen into adsorbed layers is observed at high loadings that follows a regular progression determined primarily by geometric considerations. The formation of an adsorbate core at the center of the nanotube is found to increase the self-diffusion of nitrogen. A "wormlike" phase is found for the adsorbed nitrogen in the (15, 0) carbon nanotube at high loadings and at 100 K.

Self-diffusion in a system of interacting Langevin particles

The behavior of the self-diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature beta and the particle density rho. The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small beta and rhobeta constants. The one-loop result can also be resummed using a semiphenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signaled by the vanishing of the diffusion constant, possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.

Tagged particle motion in a dense liquid: feedback effects from the collective dynamics

The nature of the tagged particle motion in the strongly correlated state of a dense liquid is studied with the self-consistent mode-coupling model. The tagged particle time correlation function psi(s)(q,t) is computed by taking into account the nonlinear feedback effects on its dynamics from the coupling with density fluctuations. We consider the two cases where (a) the short-time dynamics is diffusive resembling colloidal system and (b) the short-time dynamics is Newtonian as in an atomic system. The non-Gaussian parameter alpha(2)(t) is evaluated using the fourth- and second-order spatial moments of the van Hove self-correlation function G(s)(r,t). We observe a two-peaked structure of alpha(2)(t) for both (a) and (b) types of dynamics. We also compare other characteristic aspects of tagged particle dynamics such as the mean square displacement, non-Gaussian nature of G(s)(r,t), and fraction of mobile particles. A qualitative comparison is drawn between the theoretical results with the experimental and computer simulation results on colloids.

Dynamic scaling and freezing criteria in quasi-two-dimensional dispersions

We report on a Brownian dynamics simulation study of quasi-two-dimensional dispersions of colloidal spheres interacting by long-range electrostatic and dipolar magnetic forces. The calculated dynamic correlation functions are shown to obey dynamic scaling in terms of a characteristic relaxation time related to the mean particle distance and, due to hydrodynamic interactions, to the particle size. The dynamical freezing criterion of Löwen [Phys. Rev. E 53, R29 (1996)] is shown to be equivalent to a two-dimensional static freezing criterion.

Diffusion of hard disks and rodlike molecules on surfaces

We study the submonolayer diffusion of hard disks and rodlike molecules on smooth surfaces through numerical simulations and theoretical arguments. We concentrate on the behavior of the various diffusion coefficients as a function of the two-dimensional (2D) number density rho in the case where there are no explicit surface-particle interactions. For the hard disk case, we find that while the tracer diffusion coefficient D(T)(rho) decreases monotonically up to the freezing transition, the collective diffusion coefficient D(C)(rho) is wholly determined by the inverse compressibility which increases rapidly on approaching freezing. We also study memory effects associated with tracer diffusion, and present theoretical estimates of D(T)(rho) from the mode-mode coupling approximation. In the case of rigid rods with short-range repulsion and no orientational ordering, we find behavior very similar to the case of disks with the same repulsive interaction. Both D(T)(rho) and the angular diffusion coefficient D(R)(rho) decrease with rho. Also in this case D(C)(rho) is determined by inverse compressibility and increases rapidly close to freezing. This is in contrast to the case of flexible chainlike molecules in the lattice-gas limit, where D(C)(rho) first increases and then decreases as a function of the density due to the interplay between compressibility and mobility.