K. Nelissen

Single-file diffusion of interacting particles in a one-dimensional channel

Molecular diffusion in unidimensional channel structures (single-file diffusion) is important to understand the behavior of, e.g., colloidal particles in porous materials (zeolites) and superconducting vortices in 1-dimensional (1D) channels. Here the diffusion of charged massive particles in a 1D channel is investigated using the Langevin Dynamics (LD) simulations. We analyze different regimes based on the hierarchy of the interactions and damping mechanisms in the system and we show that, contrary to previous findings, single-file diffusion depends on the inter-particle interaction and could be suppressed if the interaction is strong enough displaying a subdiffusive behavior slower than t1/2, in agreement with recent experimental observations in colloids and charged metallic balls.

Transition from single-file to two-dimensional diffusion of interacting particles in a quasi-one-dimensional channel.

Diffusive properties of a monodisperse system of interacting particles confined to a quasi-one-dimensional channel are studied using molecular dynamics simulations. We calculate numerically the mean-squared displacement (MSD) and investigate the influence of the width of the channel (or the strength of the confinement potential) on diffusion in finite-size channels of different shapes (i.e., straight and circular). The transition from single-file diffusion to the two-dimensional diffusion regime is investigated. This transition [regarding the calculation of the scaling exponent (α) of the MSD (Δx(2)(t) ∝ t(α)] as a function of the width of the channel is shown to change depending on the channels confinement profile. In particular, the transition can be either smooth (i.e., for a parabolic confinement potential) or rather sharp (i.e., for a hard-wall potential), as distinct from infinite channels where this transition is abrupt. This result can be explained by qualitatively different distributions of the particle density for the different confinement potentials.

Induced order and re-entrant melting in classical two-dimensional binary clusters

A binary system of classical charged particles interacting through a dipole repulsive potential and confined in a two-dimensional hard-wall trap is studied by Brownian dynamics simulations. We found that the presence of small particles stabilizes the angular order of the system as a consequence of radial fluctuations of the small particles. There is an optimum in the increased rigidity of the cluster as function of the number of small particles. The small (i.e. defect) particles melt at a lower temperature compared to the big particles and exhibit a re-entrant behavior in its radial order that is induced by the intershell rotation of the big particles.

Diffusion of Interacting Particles in Discrete Geometries

We evaluate the self-diffusion and transport diffusion of interacting particles in a discrete geometry consisting of a linear chain of cavities, with interactions within a cavity described by a free-energy function. Exact analytical expressions are obtained in the absence of correlations, showing that the self-diffusion can exceed the transport diffusion if the free-energy function is concave. The effect of correlations is elucidated by comparison with numerical results. Quantitative agreement is obtained with recent experimental data for diffusion in a nanoporous zeolitic imidazolate framework material, ZIF-8.

Dynamics of topological defects and the effects of the cooling rate on finite-size two-dimensional screened Coulomb clusters

The formation of dislocations, disclinations and their dynamics is central to our understanding of crystalline materials. Here, the dynamics of these topological defects in two-dimensional (2D) clusters of charged classical particles interacting through a screened Coulomb potential is investigated through the molecular-dynamics (MD) simulation technique. The particles are confined by a harmonic potential and coupled to an Anderson heat reservoir. We investigate cooling rate effects on the defect dynamics by decreasing the temperature of the heat reservoir linear in time. We found that: i) the mobility of the defects strongly depends on the number of nearest neighbors and the nature of those defects, ii) geometrically induced defects have different dynamics than other defects because of spontaneous pinning of the defects at the corners of the hexagon, and iii) if the cooling speed is large enough, the system ends up in a non-equilibrium state and a glass-like structure is formed.

Hysteresis and reentrant melting of a self-organized system of classical particles confined in a parabolic trap

The melting of a self-organized system composed of classical particles confined in a two-dimensional parabolic trap and interacting through a potential with a short-range attractive part and a long-range repulsive potential is studied. Different behaviors of the melting temperature are found depending on the strength (B) of the attractive part of the interparticle potential. The melting of a system consisting of small bubbles takes place through a two-step melting process. A reentrant behavior and a thermally induced structural phase transition are observed in a small region of the (B,kappa) space. A hysteresis effect in the configuration of the particles is observed as a function of temperature. This is a consequence of the presence of a potential barrier between different configurations of the system.

Diffusion of interacting particles in discrete geometries: Equilibrium and dynamical properties.

We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.110601]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their behavior is similar to that of interacting particles in porous materials. Different expressions for the particle jump rates are derived from transition-state theory. Which expression should be used depends on the strength of the interparticle interactions. Analytical expressions for the self- and transport diffusion are derived when correlations, caused by memory effects in the environment, are neglected. The diffusive behavior is studied numerically with kinetic Monte Carlo (kMC) simulations, which reproduces the diffusion including correlations. The effect of correlations is studied by comparing the analytical expressions with the kMC simulations. It is found that the Maxwell-Stefan diffusion can exceed the self-diffusion. To our knowledge, this is the first time this is observed. The diffusive behavior in one-dimensional and higher-dimensional systems is qualitatively the same, with the effect of correlations decreasing for increasing dimension. The length dependence of both the self- and transport diffusion is studied for one-dimensional systems. For long lengths the self-diffusion shows a 1/L dependence. Finally, we discuss when agreement with experiments and simulations can be expected. The assumption that particles in different cavities do not interact is expected to hold quantitatively at low and medium particle concentrations if the particles are not strongly interacting.

Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study

We use kinetic Monte Carlo simulations to investigate current fluctuations in boundary driven generalized exclusion processes, in different dimensions. Simulation results are in full agreement with predictions based on the additivity principle and the macroscopic fluctuation theory. The current statistics are independent of the shape of the contacts with the reservoirs, provided they are macroscopic in size. In general, the current distribution depends on the spatial dimension. For the special cases of the symmetric simple exclusion process and the zero-range process, the current statistics are the same for all spatial dimensions.

Adsorption and desorption in confined geometries : a discrete hopping model

We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at different rates, and are strongly influenced by the concentration-dependent transport diffusion. Analytical solutions for the transport and self-diffusion are given for systems of length 1 and 2 and for a zero-range process. In the last situation the self- and transport diffusion can be calculated analytically for any length.

Work and dissipation in 2D clusters

We show by extensive numerical simulations, that far-from-equilibrium experiments on dusty plasmas and on dipole particles in a circular cavity are good candidates for the verification of the Jarzynski equality, the Crooks relation and, to a lesser extent, of the recently obtained microscopic expression for the dissipated work.