Mass Transfer in a Nanoscale Material Enhanced by an Opposing Flux

Chmelik, Christian; Bux, Helge; Caro, Jürgen; Heinke, Lars; Hibbe, Florian; Titze, Tobias; Kärger, Jörg

doi:10.1103/physrevlett.104.085902

Cited by 118 publications

(157 citation statements)

References 22 publications

Supporting

Mentioning

141

Contrasting

Unclassified

Order By: Relevance

“…Noteworthy is the fact that the transport diffusion shows a minimum when the thermodynamic factor is around its maximum. This feature is in agreement with experimental observations [20,34,35] and with MD simulations [36]. It is now easily understood: when Γ −1 is at its highest, the tendency to cluster is maximal, therefore the force opposing the current is also at its strongest.…”

supporting

confidence: 91%

“…Correlations have noticeable effect, and are now more important for D t than for D s . Notice that in all cases correlations lower the diffusion coefficients.Motivated by the qualitative agreement with experiments, we have tried to reproduce the experimental results from [20] quantitatively. Inspired by the form of the energy function for Lennard-Jones crystals [38], we take βf (n) = an 2 + bn 3 for n ≤ n max , with n max = 13 taken from the experimental data [39].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Diffusion of Interacting Particles in Discrete Geometries

et al. 2013

View full text Add to dashboard Cite

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 ...

show abstract

supporting

confidence: 91%

mentioning

confidence: 99%

Diffusion of Interacting Particles in Discrete Geometries

et al. 2013

View full text Add to dashboard Cite

show abstract

“…In another MOF material, ZIF-8, an interesting phenomenon, namely the enhancement of the mass transfer by the flux of molecules in an opposite direction has been discovered. 57 …”

Section: Adsorbates: Orientation and Diffusionmentioning

confidence: 99%

Infrared and Raman imaging of heterogeneous catalysts

2010

View full text Add to dashboard Cite

“…For interacting particles, the transport diffusion is in general different from the self-diffusion coefficient D s [19,20], which measures the average mean square displacement (MSD) of a single particle in equilibrium. In one dimension it is defined as:…”

Section: Analytical Solutions For the Diffusionmentioning

confidence: 99%

Adsorption and desorption in confined geometries: A discrete hopping model

Becker

Nelissen

Cleuren

et al. 2014

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

Abstract. 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.

show abstract

Mass Transfer in a Nanoscale Material Enhanced by an Opposing Flux

Cited by 118 publications

References 22 publications

Diffusion of Interacting Particles in Discrete Geometries

Diffusion of Interacting Particles in Discrete Geometries

Infrared and Raman imaging of heterogeneous catalysts

Adsorption and desorption in confined geometries: A discrete hopping model

Contact Info

Product

Resources

About