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.PACS numbers: 05.40. Jc, 05.60.Cd, 66.30.Pa The equality of inertial and gravitational mass played a crucial role in Einstein's discovery of general relativity. Similarly, Einstein's work on Brownian motion is based on the identity of the transport-and self-diffusion coefficients for noninteracting particles [1], leading eventually through Perrin's experiments [2] to the vindication of the atomic hypothesis. In general, however, diffusion of interacting particles is described by two different coefficients. The transport-diffusion coefficient D t quantifies the particle flux j appearing in response to a concentration gradient dc/dx:The self-diffusion coefficient D s describes the mean squared displacement of a single particle in a suspension of identical particles at equilibrium: x 2 (t) ∝ D s t. An alternative way for measuring this coefficient is by labeling, in this system at equilibrium, a subset of these particles (denoted by * ) in a way to create a concentration gradient dc * /dx of labeled particles under overall equilibrium conditions. The resulting flux j * of these particles reads:Both forms of diffusion have been studied in a wide variety of physical contexts, including continuum [3][4][5][6][7][8][9][10] and lattice [11][12][13] models. Exact analytical results for the diffusion coefficient of interacting particles are however typically limited to a perturbation expansion, for example in the density of the particles. The effect of correlations is notoriously difficult to evaluate in continuum models, especially when hydrodynamic interactions come into play, while they can play a dominant role, for example, in lattice models with particle exclusion constraints.In this Letter, we introduce a physically relevant model, for which exact analytical results can be obtained at all values of the concentration and for any interaction. It describes the diffusive hopping of interacting particles in a compartmentalized system, see Fig. 1 for a schematic representation. It is assumed that the relaxation inside each cavity is fast enough to establish a local equilibrium, described by a free-energy function characterizing the confinement and interaction of the particles. This model describes diffusion in confined geometries [14]. Of particular interest are microporous materials [15,16] [21][22][23][24][25][26], it was found that the self-diffusion could exceed the transport diffusion, a result confirmed by ...

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 t 1/2 , in agreement with recent experimental observations in colloids and charged metallic balls.

The properties and applications of metallic nanoparticles are inseparably connected not only to their detailed morphology and composition, but also to their structural configuration and mutual interactions. As a result, the assemblies often have superior properties as compared to individual nanoparticles. Although it has been reported that nanoparticles can form highly symmetric clusters, if the configuration can be predicted as a function of the synthesis parameters, more targeted and accurate synthesis will be possible. We present here a theoretical model that accurately predicts the structure and configuration of self-assembled gold nanoclusters. The validity of the model is verified using quantitative experimental data extracted from electron tomography 3D reconstructions of different assemblies. The present theoretical model is generic and can in principle be used for different types of nanoparticles, providing a very wide window of potential applications.

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 channel's 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.