Determination of surface diffusion coefficients by Monte Carlo methods: Comparison of fluctuation and Kubo–Green methods

Uebing, C.; Gomer, R.

doi:10.1063/1.466819

Cited by 70 publications

(52 citation statements)

References 13 publications

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“…The self-diffusivity is also known as the tracer diffusivity. 33 The transport diffusivity is also referred to as the Fickian diffusivity, 53 the chemical diffusivity, 54 or the collective diffusivity. 55 Finally, the corrected diffusivity is also known as the jump diffusivity.…”

Section: ͑11͒mentioning

confidence: 99%

Knudsen self- and Fickian diffusion in rough nanoporous media

Malek

Coppens

2003

The Journal of Chemical Physics

247

147

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The effect of pore surface roughness on Knudsen diffusion in nanoporous media is investigated by dynamic Monte Carlo simulations and analytical calculations. A conceptual difference is found between the roughness dependence of the macroscopic, transport diffusivity and the microscopic, self-diffusivity, which is reminiscent of diffusion in zeolites, where a similar difference arises due to adsorption effects and intermolecular interactions. Because of the dependence of the self-diffusivity on molecular residence times, self-diffusion may be roughness dependent, while transport diffusion is not. Detailed proofs are given. The differences become significant when the pore surface is rough down to molecular scales, as is the case, e.g., for many common sol-gel materials. Simulations are in good agreement with analytical calculations for several tested rough, fractal pore structures. These results are important for the interpretation of experimental diffusion measurements and for the study of diffusion-reaction processes in nanoporous catalysts with a rough internal surface.

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Section: ͑11͒mentioning

confidence: 99%

Knudsen self- and Fickian diffusion in rough nanoporous media

Malek

Coppens

2003

The Journal of Chemical Physics

247

147

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“…22,23 Monte Carlo simulations show that jump and tracer diffusion coefficients are practically identical in a broad interval of carrier densities and temperatures. 24 Hence, we assume hereafter D* = D J . The jump diffusion coefficient can often be expressed as [24][25][26] …”

Section: Definition Of Diffusion Coefficientmentioning

confidence: 99%

“…24 Hence, we assume hereafter D* = D J . The jump diffusion coefficient can often be expressed as [24][25][26] …”

Section: Definition Of Diffusion Coefficientmentioning

confidence: 99%

Interpretation of diffusion coefficients in nanostructured materials from random walk numerical simulation

Anta

Mora‐Seró

Dittrich

et al. 2008

Phys. Chem. Chem. Phys.

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We make use of the numerical simulation random walk (RWNS) method to compute the ''jump'' diffusion coefficient of electrons in nanostructured materials via mean-square displacement. First, a summary of analytical results is given that relates the diffusion coefficient obtained from RWNS to those in the multiple-trapping (MT) and hopping models. Simulations are performed in a three-dimensional lattice of trap sites with energies distributed according to an exponential distribution and with a step-function distribution centered at the Fermi level. It is observed that once the stationary state is reached, the ensemble of particles follow Fermi-Dirac statistics with a well-defined Fermi level. In this stationary situation the diffusion coefficient obeys the theoretical predictions so that RWNS effectively reproduces the MT model. Mobilities can be also computed when an electrical bias is applied and they are observed to comply with the Einstein relation when compared with steady-state diffusion coefficients. The evolution of the system towards the stationary situation is also studied. When the diffusion coefficients are monitored along simulation time a transition from anomalous to trap-limited transport is observed. The nature of this transition is discussed in terms of the evolution of electron distribution and the Fermi level. All these results will facilitate the use of RW simulation and related methods to interpret steady-state as well as transient experimental techniques.

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“…40,48 Monte Carlo simulations show that jump and tracer diffusion coefficient are practically identical in many conditions. 54 The jump diffusion coefficient can often be expressed as 38,39,45 …”

Section: Diffusion Coefficientsmentioning

confidence: 99%

“…106 and 107. In equilibrium the transport is governed by the fastest hop of a charge carrier. The most probable upward jump corresponds to an optimized combination of the distance and energy difference, eqn (54). Let a = N À1/3 L be the mean distance between localized sites.…”

Section: Hopping In Exponential Dosmentioning

confidence: 99%

Interpretation of electron diffusion coefficient in organic and inorganic semiconductors with broad distributions of states

Bisquert

2008

Phys. Chem. Chem. Phys.

184

175

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The carrier transport properties in nanocrystalline semiconductors and organic materials play a key role for modern organic/inorganic devices such as dye-sensitized (DSC) and organic solar cells, organic and hybrid light-emitting diodes (OLEDs), organic field-effect transistors, and electrochemical sensors and displays. Carrier transport in these materials usually occurs by transitions in a broad distribution of localized states. As a result the transport is dominated by thermal activation to a band of extended states (multiple trapping), or if these do not exist, by hopping via localized states. We provide a general view of the physical interpretation of the variations of carrier transport coefficients (diffusion coefficient and mobility) with respect to the carrier concentration, or Fermi level, examining in detail models for carrier transport in nanocrystalline semiconductors and organic materials with the following distributions: single and two-level systems, exponential and Gaussian density of states. We treat both the multiple trapping models and the hopping model in the transport energy approximation. The analysis is simplified by thermodynamic properties: the chemical capacitance, C m , and the thermodynamic factor, w n , that allow us to derive many properties of the chemical diffusion coefficient, D n , used in Fick's law. The formulation of the generalized Einstein relation for the mobility to diffusion ratio shows that the carrier mobility is proportional to the jump diffusion coefficient, D J , that is derived from single particle random walk. Characteristic experimental data for nanocrystalline TiO 2 in DSC and electrochemically doped conducting polymers are discussed in the light of these models.

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Determination of surface diffusion coefficients by Monte Carlo methods: Comparison of fluctuation and Kubo–Green methods

Cited by 70 publications

References 13 publications

Knudsen self- and Fickian diffusion in rough nanoporous media

Knudsen self- and Fickian diffusion in rough nanoporous media

Interpretation of diffusion coefficients in nanostructured materials from random walk numerical simulation

Interpretation of electron diffusion coefficient in organic and inorganic semiconductors with broad distributions of states

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